Marco has been saving his loose change for the past month. When Marco took his change to the bank, he received $11.42. He knows he had 83 coins in all. There were 18 nickels, 7 pennies, and the rest were quarters and dimes. To find out the number of quarters he had, Marco set up and solved the system of equations shown below. I + y = 58 0.10x +0.25y = 10.45 %3D How many quarters did Marco have? O 10 O 25 O 31 O 27

Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Marco has been saving his loose change for the past month. When Marco took his
change to the bank, he received $11.42. He knows he had 83 coins in all. There were 18
nickels, 7 pennies, and the rest were quarters and dimes. To find out the number of
quarters he had, Marco set up and solved the system of equations shown below.
T+y=58
0.10x + 0.25y = 10.45
How many quarters did Marco have?
O 10
O 25
O 31
O 27
Chp
Transcribed Image Text:Marco has been saving his loose change for the past month. When Marco took his change to the bank, he received $11.42. He knows he had 83 coins in all. There were 18 nickels, 7 pennies, and the rest were quarters and dimes. To find out the number of quarters he had, Marco set up and solved the system of equations shown below. T+y=58 0.10x + 0.25y = 10.45 How many quarters did Marco have? O 10 O 25 O 31 O 27 Chp
Expert Solution
Step 1

Given:

The system of equation is 

x+y=580.10x+0.25y=10.45

Solution:

it can be observed that  x is dimes and y is quarters because in second equation 0.25 is multiplied with y and 1 quarters worth 25 cents.

The value of y can be obtained from equation x+y=58 is

y=58-x

Substitute y=58-x in 0.10x+0.25y=10.45 to obtain x as,

0.10x+0.2558-x=10.450.10x+14.5-0.25x=10.45-0.15x=-4.05x=27

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