To state: The weight of each alloy, in grams, that is required to produce 80g of a new alloy that is 34% silver if the amount of 30% alloy is twice the amount of 22% alloy used. Stewart’s Metals has three silver alloys, first is 22% silver, another is 30% silver, and the third is 42% silver.

The weight of each alloy is 14.55g of the first alloy, 29.10g of the second alloy, and 36.35 of the third alloy.

Given information:

Stewart’s Metals ha three silver alloys, first is 22% silver, another is 30% silver, and the third is 42% silver.

Explanation:

Let’s take x as the number of grams of the 22% silver alloy, y as the number of grams of the 30% silver alloy, and z as the number of grams of the 42% silver alloy.

Now make equations using the given information.

Total amount of the new alloy is 80g which consists of all the given three alloys:

x+y+z=80

New alloy contains 34% silver:

0.22x+0.30y+0.42z=0.34800.22x+0.30y+0.42z=27.2

In the new alloy, the amount of 30% alloy is twice the amount of 22% alloy used: y=2x

The three equations are:

x+y+z=80⋯10.22x+0.30y+0.42z=27.2⋯2y=2x⋯3

Multiply the first equation by -0.42,

x+y+z=80×−0.42−0.42x−0.42y−0.42z=−33.6⋯4

Now add equations (2) and (4),

−0.42x−0.42y−0.42z=−33.6 0.22x+0.30y+0.42z=27.2¯ −0.20x−0.12y=−0.64

Substitute the value of y=2x in −0.20x−0.12y=−0.64 ,

−0.20x−0.122x=−0.64−0.20x−0.24x=−0.64−0.44x=−0.64x=14.55

Now substitute the value of x=14.55 in y=2x ,

y=2xy=214.55y=29.10

Now substitute the values of x and y in equation (1),

x+y+z=8014.55+29.10+z=80z=36.35

Therefore, the weight of each alloy, in grams, that is required to produce 80g of a new alloy that is 34% silver is 14.55g of the first alloy, 29.10g of the second alloy, and 36.35g of the third alloy.

Chapter 7.3, Problem 89E

Chapter 7.3, Problem 91E

Chapter 7 Solutions

PRECALCULUS:GRAPHICAL,...-NASTA ED.

Ch. 7.1 - Prob. 1QR Ch. 7.1 - Prob. 2QR Ch. 7.1 - Prob. 3QR Ch. 7.1 - Prob. 4QR Ch. 7.1 - Prob. 5QR Ch. 7.1 - Prob. 6QR Ch. 7.1 - Prob. 7QR Ch. 7.1 - Prob. 8QR Ch. 7.1 - Prob. 9QR Ch. 7.1 - Prob. 10QR

Ch. 7.1 - Prob. 1E Ch. 7.1 - Prob. 2E Ch. 7.1 - Prob. 3E Ch. 7.1 - Prob. 4E Ch. 7.1 - Prob. 5E Ch. 7.1 - Prob. 6E Ch. 7.1 - Prob. 7E Ch. 7.1 - Prob. 8E Ch. 7.1 - Prob. 9E Ch. 7.1 - Prob. 10E Ch. 7.1 - Prob. 11E Ch. 7.1 - Prob. 12E Ch. 7.1 - Prob. 13E Ch. 7.1 - Prob. 14E Ch. 7.1 - Prob. 15E Ch. 7.1 - Prob. 16E Ch. 7.1 - Prob. 17E Ch. 7.1 - Prob. 18E Ch. 7.1 - Prob. 19E Ch. 7.1 - Prob. 20E Ch. 7.1 - Prob. 21E Ch. 7.1 - Prob. 22E Ch. 7.1 - Prob. 23E Ch. 7.1 - Prob. 24E Ch. 7.1 - Prob. 25E Ch. 7.1 - Prob. 26E Ch. 7.1 - Prob. 27E Ch. 7.1 - Prob. 28E Ch. 7.1 - Prob. 29E Ch. 7.1 - Prob. 30E Ch. 7.1 - Prob. 31E Ch. 7.1 - Prob. 32E Ch. 7.1 - Prob. 33E Ch. 7.1 - Prob. 34E Ch. 7.1 - Prob. 35E Ch. 7.1 - Prob. 36E Ch. 7.1 - Prob. 37E Ch. 7.1 - Prob. 38E Ch. 7.1 - Prob. 39E Ch. 7.1 - Prob. 40E Ch. 7.1 - Prob. 41E Ch. 7.1 - Prob. 42E Ch. 7.1 - Prob. 43E Ch. 7.1 - Prob. 44E Ch. 7.1 - Prob. 45E Ch. 7.1 - Prob. 46E Ch. 7.1 - Prob. 47E Ch. 7.1 - Prob. 48E Ch. 7.1 - Prob. 49E Ch. 7.1 - Prob. 50E Ch. 7.1 - Prob. 51E Ch. 7.1 - Prob. 52E Ch. 7.1 - Prob. 53E Ch. 7.1 - Prob. 54E Ch. 7.1 - Prob. 55E Ch. 7.1 - Prob. 56E Ch. 7.1 - Prob. 57E Ch. 7.1 - Prob. 58E Ch. 7.1 - Prob. 59E Ch. 7.1 - Prob. 60E Ch. 7.1 - Prob. 61E Ch. 7.1 - Prob. 62E Ch. 7.1 - Prob. 63E Ch. 7.1 - Prob. 64E Ch. 7.1 - Prob. 65E Ch. 7.1 - Prob. 66E Ch. 7.1 - Prob. 67E Ch. 7.1 - Prob. 68E Ch. 7.1 - Prob. 69E Ch. 7.1 - Prob. 70E Ch. 7.2 - Prob. 1QR Ch. 7.2 - Prob. 2QR Ch. 7.2 - Prob. 3QR Ch. 7.2 - Prob. 4QR Ch. 7.2 - Prob. 5QR Ch. 7.2 - Prob. 6QR Ch. 7.2 - Prob. 7QR Ch. 7.2 - Prob. 8QR Ch. 7.2 - Prob. 9QR Ch. 7.2 - Prob. 10QR Ch. 7.2 - Prob. 1E Ch. 7.2 - Prob. 2E Ch. 7.2 - Prob. 3E Ch. 7.2 - Prob. 4E Ch. 7.2 - Prob. 5E Ch. 7.2 - Prob. 6E Ch. 7.2 - Prob. 7E Ch. 7.2 - Prob. 8E Ch. 7.2 - Prob. 9E Ch. 7.2 - Prob. 10E Ch. 7.2 - Prob. 11E Ch. 7.2 - Prob. 12E Ch. 7.2 - Prob. 13E Ch. 7.2 - Prob. 14E Ch. 7.2 - Prob. 15E Ch. 7.2 - Prob. 16E Ch. 7.2 - Prob. 17E Ch. 7.2 - Prob. 18E Ch. 7.2 - Prob. 19E Ch. 7.2 - Prob. 20E Ch. 7.2 - Prob. 21E Ch. 7.2 - Prob. 22E Ch. 7.2 - Prob. 23E Ch. 7.2 - Prob. 24E Ch. 7.2 - Prob. 25E Ch. 7.2 - Prob. 26E Ch. 7.2 - Prob. 27E Ch. 7.2 - Prob. 28E Ch. 7.2 - Prob. 29E Ch. 7.2 - Prob. 30E Ch. 7.2 - Prob. 31E Ch. 7.2 - Prob. 32E Ch. 7.2 - Prob. 33E Ch. 7.2 - Prob. 34E Ch. 7.2 - Prob. 35E Ch. 7.2 - Prob. 36E Ch. 7.2 - Prob. 37E Ch. 7.2 - Prob. 38E Ch. 7.2 - Prob. 39E Ch. 7.2 - Prob. 40E Ch. 7.2 - Prob. 41E Ch. 7.2 - Prob. 42E Ch. 7.2 - Prob. 43E Ch. 7.2 - Prob. 44E Ch. 7.2 - Prob. 45E Ch. 7.2 - Prob. 46E Ch. 7.2 - Prob. 47E Ch. 7.2 - Prob. 48E Ch. 7.2 - Prob. 49E Ch. 7.2 - Prob. 50E Ch. 7.2 - Prob. 51E Ch. 7.2 - Prob. 52E Ch. 7.2 - Prob. 53E Ch. 7.2 - Prob. 54E Ch. 7.2 - Prob. 55E Ch. 7.2 - Prob. 56E Ch. 7.2 - Prob. 57E Ch. 7.2 - Prob. 58E Ch. 7.2 - Prob. 59E Ch. 7.2 - Prob. 60E Ch. 7.2 - Prob. 61E Ch. 7.2 - Prob. 62E Ch. 7.2 - Prob. 63E Ch. 7.2 - Prob. 64E Ch. 7.2 - Prob. 65E Ch. 7.2 - Prob. 66E Ch. 7.2 - Prob. 67E Ch. 7.2 - Prob. 68E Ch. 7.2 - Prob. 69E Ch. 7.2 - Prob. 70E Ch. 7.2 - Prob. 71E Ch. 7.2 - Prob. 72E Ch. 7.2 - Prob. 73E Ch. 7.3 - Prob. 1QR Ch. 7.3 - Prob. 2QR Ch. 7.3 - Prob. 3QR Ch. 7.3 - Prob. 4QR Ch. 7.3 - Prob. 5QR Ch. 7.3 - Prob. 6QR Ch. 7.3 - Prob. 7QR Ch. 7.3 - Prob. 8QR Ch. 7.3 - Prob. 9QR Ch. 7.3 - Prob. 10QR Ch. 7.3 - Prob. 1E Ch. 7.3 - Prob. 2E Ch. 7.3 - Prob. 3E Ch. 7.3 - Prob. 4E Ch. 7.3 - Prob. 5E Ch. 7.3 - Prob. 6E Ch. 7.3 - Prob. 7E Ch. 7.3 - Prob. 8E Ch. 7.3 - Prob. 9E Ch. 7.3 - Prob. 10E Ch. 7.3 - Prob. 11E Ch. 7.3 - Prob. 12E Ch. 7.3 - Prob. 13E Ch. 7.3 - Prob. 14E Ch. 7.3 - Prob. 15E Ch. 7.3 - Prob. 16E Ch. 7.3 - Prob. 17E Ch. 7.3 - Prob. 18E Ch. 7.3 - Prob. 19E Ch. 7.3 - Prob. 20E Ch. 7.3 - Prob. 21E Ch. 7.3 - Prob. 22E Ch. 7.3 - Prob. 23E Ch. 7.3 - Prob. 24E Ch. 7.3 - Prob. 25E Ch. 7.3 - Prob. 26E Ch. 7.3 - Prob. 27E Ch. 7.3 - Prob. 28E Ch. 7.3 - Prob. 29E Ch. 7.3 - Prob. 30E Ch. 7.3 - Prob. 31E Ch. 7.3 - Prob. 32E Ch. 7.3 - Prob. 33E Ch. 7.3 - Prob. 34E Ch. 7.3 - Prob. 35E Ch. 7.3 - Prob. 36E Ch. 7.3 - Prob. 37E Ch. 7.3 - Prob. 38E Ch. 7.3 - Prob. 39E Ch. 7.3 - Prob. 40E Ch. 7.3 - Prob. 41E Ch. 7.3 - Prob. 42E Ch. 7.3 - Prob. 43E Ch. 7.3 - Prob. 44E Ch. 7.3 - Prob. 45E Ch. 7.3 - Prob. 46E Ch. 7.3 - Prob. 47E Ch. 7.3 - Prob. 48E Ch. 7.3 - Prob. 49E Ch. 7.3 - Prob. 50E Ch. 7.3 - Prob. 51E Ch. 7.3 - Prob. 52E Ch. 7.3 - Prob. 53E Ch. 7.3 - Prob. 54E Ch. 7.3 - Prob. 55E Ch. 7.3 - Prob. 56E Ch. 7.3 - Prob. 57E Ch. 7.3 - Prob. 58E Ch. 7.3 - Prob. 59E Ch. 7.3 - Prob. 60E Ch. 7.3 - Prob. 61E Ch. 7.3 - Prob. 62E Ch. 7.3 - Prob. 63E Ch. 7.3 - Prob. 64E Ch. 7.3 - Prob. 65E Ch. 7.3 - Prob. 66E Ch. 7.3 - Prob. 67E Ch. 7.3 - Prob. 68E Ch. 7.3 - Prob. 69E Ch. 7.3 - Prob. 70E Ch. 7.3 - Prob. 71E Ch. 7.3 - Prob. 72E Ch. 7.3 - Prob. 73E Ch. 7.3 - Prob. 74E Ch. 7.3 - Prob. 75E Ch. 7.3 - Prob. 76E Ch. 7.3 - Prob. 77E Ch. 7.3 - Prob. 78E Ch. 7.3 - Prob. 79E Ch. 7.3 - Prob. 80E Ch. 7.3 - Prob. 81E Ch. 7.3 - Prob. 82E Ch. 7.3 - Prob. 83E Ch. 7.3 - Prob. 84E Ch. 7.3 - Prob. 85E Ch. 7.3 - Prob. 86E Ch. 7.3 - Prob. 87E Ch. 7.3 - Prob. 88E Ch. 7.3 - Prob. 89E Ch. 7.3 - Prob. 90E Ch. 7.3 - Prob. 91E Ch. 7.3 - Prob. 92E Ch. 7.3 - Prob. 93E Ch. 7.3 - Prob. 94E Ch. 7.3 - Prob. 95E Ch. 7.3 - Prob. 96E Ch. 7.3 - Prob. 97E Ch. 7.3 - Prob. 98E Ch. 7.3 - Prob. 99E Ch. 7.3 - Prob. 100E Ch. 7.3 - Prob. 101E Ch. 7.3 - Prob. 102E Ch. 7.3 - Prob. 103E Ch. 7.3 - Prob. 104E Ch. 7.3 - Prob. 105E Ch. 7.3 - Prob. 106E Ch. 7.3 - Prob. 107E Ch. 7.3 - Prob. 108E Ch. 7.3 - Prob. 109E Ch. 7.3 - Prob. 110E Ch. 7.4 - Prob. 1QR Ch. 7.4 - Prob. 2QR Ch. 7.4 - Prob. 3QR Ch. 7.4 - Prob. 4QR Ch. 7.4 - Prob. 5QR Ch. 7.4 - Prob. 6QR Ch. 7.4 - Prob. 7QR Ch. 7.4 - Prob. 8QR Ch. 7.4 - Prob. 9QR Ch. 7.4 - Prob. 10QR Ch. 7.4 - Prob. 1E Ch. 7.4 - Prob. 2E Ch. 7.4 - Prob. 3E Ch. 7.4 - Prob. 4E Ch. 7.4 - Prob. 5E Ch. 7.4 - Prob. 6E Ch. 7.4 - Prob. 7E Ch. 7.4 - Prob. 8E Ch. 7.4 - Prob. 9E Ch. 7.4 - Prob. 10E Ch. 7.4 - Prob. 11E Ch. 7.4 - Prob. 12E Ch. 7.4 - Prob. 13E Ch. 7.4 - Prob. 14E Ch. 7.4 - Prob. 15E Ch. 7.4 - Prob. 16E Ch. 7.4 - Prob. 17E Ch. 7.4 - Prob. 18E Ch. 7.4 - Prob. 19E Ch. 7.4 - Prob. 20E Ch. 7.4 - Prob. 21E Ch. 7.4 - Prob. 22E Ch. 7.4 - Prob. 23E Ch. 7.4 - Prob. 24E Ch. 7.4 - Prob. 25E Ch. 7.4 - Prob. 26E Ch. 7.4 - Prob. 27E Ch. 7.4 - Prob. 28E Ch. 7.4 - Prob. 29E Ch. 7.4 - Prob. 30E Ch. 7.4 - Prob. 31E Ch. 7.4 - Prob. 32E Ch. 7.4 - Prob. 33E Ch. 7.4 - Prob. 34E Ch. 7.4 - Prob. 35E Ch. 7.4 - Prob. 36E Ch. 7.4 - Prob. 37E Ch. 7.4 - Prob. 38E Ch. 7.4 - Prob. 39E Ch. 7.4 - Prob. 40E Ch. 7.4 - Prob. 41E Ch. 7.4 - Prob. 42E Ch. 7.4 - Prob. 43E Ch. 7.4 - Prob. 44E Ch. 7.4 - Prob. 45E Ch. 7.4 - Prob. 46E Ch. 7.4 - Prob. 47E Ch. 7.4 - Prob. 48E Ch. 7.4 - Prob. 49E Ch. 7.4 - Prob. 50E Ch. 7.4 - Prob. 51E Ch. 7.4 - Prob. 52E Ch. 7 - Prob. 1RE Ch. 7 - Prob. 2RE Ch. 7 - Prob. 3RE Ch. 7 - Prob. 4RE Ch. 7 - Prob. 5RE Ch. 7 - Prob. 6RE Ch. 7 - Prob. 7RE Ch. 7 - Prob. 8RE Ch. 7 - Prob. 9RE Ch. 7 - Prob. 10RE Ch. 7 - Prob. 11RE Ch. 7 - Prob. 12RE Ch. 7 - Prob. 13RE Ch. 7 - Prob. 14RE Ch. 7 - Prob. 15RE Ch. 7 - Prob. 16RE Ch. 7 - Prob. 17RE Ch. 7 - Prob. 18RE Ch. 7 - Prob. 19RE Ch. 7 - Prob. 20RE Ch. 7 - Prob. 21RE Ch. 7 - Prob. 22RE Ch. 7 - Prob. 23RE Ch. 7 - Prob. 24RE Ch. 7 - Prob. 25RE Ch. 7 - Prob. 26RE Ch. 7 - Prob. 27RE Ch. 7 - Prob. 28RE Ch. 7 - Prob. 29RE Ch. 7 - Prob. 30RE Ch. 7 - Prob. 31RE Ch. 7 - Prob. 32RE Ch. 7 - Prob. 33RE Ch. 7 - Prob. 34RE Ch. 7 - Prob. 35RE Ch. 7 - Prob. 36RE Ch. 7 - Prob. 37RE Ch. 7 - Prob. 38RE Ch. 7 - Prob. 39RE Ch. 7 - Prob. 40RE Ch. 7 - Prob. 41RE Ch. 7 - Prob. 42RE Ch. 7 - Prob. 43RE Ch. 7 - Prob. 44RE Ch. 7 - Prob. 45RE Ch. 7 - Prob. 46RE Ch. 7 - Prob. 47RE Ch. 7 - Prob. 48RE Ch. 7 - Prob. 49RE Ch. 7 - Prob. 50RE Ch. 7 - Prob. 51RE Ch. 7 - Prob. 52RE Ch. 7 - Prob. 53RE Ch. 7 - Prob. 54RE Ch. 7 - Prob. 55RE Ch. 7 - Prob. 56RE Ch. 7 - Prob. 57RE Ch. 7 - Prob. 58RE Ch. 7 - Prob. 59RE Ch. 7 - Prob. 60RE Ch. 7 - Prob. 61RE Ch. 7 - Prob. 62RE Ch. 7 - Prob. 63RE Ch. 7 - Prob. 64RE Ch. 7 - Prob. 65RE Ch. 7 - Prob. 66RE Ch. 7 - Prob. 67RE Ch. 7 - Prob. 68RE Ch. 7 - Prob. 69RE Ch. 7 - Prob. 70RE Ch. 7 - Prob. 71RE Ch. 7 - Prob. 72RE Ch. 7 - Prob. 73RE Ch. 7 - Prob. 74RE Ch. 7 - Prob. 75RE Ch. 7 - Prob. 76RE Ch. 7 - Prob. 77RE Ch. 7 - Prob. 78RE Ch. 7 - Prob. 79RE Ch. 7 - Prob. 80RE Ch. 7 - Prob. 81RE

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