Chapter 2, Problem 2ALQ

You go to a convenience store to buy candy and find the owner to be rather odd. He allows you to buy pieces only in multiples of tour, and to buy four, you need $0.23. He allows you only to use 3 pennies and 2 dimes. You have a bunch of pennies and dimes, and instead of counting them, you decide to weigh them. You have 636.3 g of pennies, and each penny weighs an average of 3.03 g. Each dime weighs an average of 2.29 g. Each piece of candy weighs an average of 10.23 g.

1. How many pennies do you have?
2. How many dimes do you need to buy as much candy as possible?
3. How much would all of your dimes weigh?
4. How many pieces of candy could you buy (based on the number of dimes from part b)?
5. How much would this candy weigh?
6. How many pieces of candy could you buy with twice as many dimes?

Interpretation Introduction

(a)

Interpretation:

Number of pennies on hand should to be calculated ·

Concept Introduction:

An arithmetical multiplier which is used for converting a quantity expressed in one unit into another equivalent set of units is said to be conversion factor.

Answer to Problem 2ALQ

There are $210$ pennies on hand.

Explanation of Solution

Total weight of the pennies are product of single unit of pennies ·

Following equation can be applied for solving problem ·

${\text{x}}_1=\frac{{\text{t}}_1}{{\text{d}}_1}$

Where,

${\text{x}}_1$ represents number of pennies on the hand ·

${\text{t}}_1$ represents total weight of pennies on hand ·

${\text{d}}_1$ represents the average weight of a penny ·

Total weight of pennies on the hand is equals to $636·3\text{g}$

Average weight of a penny is equals to $3·03\text{g}$

Substitute $636·3\text{g}$ for number of pennies and $3·03$ for average weight of penny

$\begin{array}{l}{\text{x}}_1=\frac{{\text{t}}_1}{{\text{d}}_1}\\ {\text{x}}_1=\frac{636·3\text{g}}{3·03\text{g}}\\ {\text{x}}_1=210\end{array}$

There are $210$ pennies on the hand·

Interpretation Introduction

(b)

Interpretation:

Number of dimes need to buy candies as much as possible should be calculated.

Concept Introduction:

An arithmetical multiplier which is used for converting a quantity expressed in one unit into another equivalent set of units is said to be conversion factor.

Answer to Problem 2ALQ

There should be $140$ dimes to buy candies as much as possible.

Explanation of Solution

Seller is accepting only 3 pennies and 2 dimes. There are 210 pennies on the hand, therefore dimes can be used to buy can be calculated according to following equation.

${\text{y}}_1=\frac{{\text{x}}_1}{3}\times 2$

Where ,

${\text{y}}_1$ represents number of dimes should be needed to buy candies ·

${\text{x}}_1$ represents number of pennies on the hand·

Substitute $210$ for number of pennies on the hand·

$\begin{array}{l}{\text{y}}_1=\frac{{\text{x}}_1}{3}\times 2\\ {\text{y}}_1=\frac{210}{3}\times 2\\ 2{\text{y}}_1=140\end{array}$

There should be $140$ dimes to buy candies as much as possible.

Interpretation Introduction

(c)

Interpretation:

Weight of all dimes should be calculated.

Concept Introduction:

An arithmetical multiplier which is used for converting a quantity expressed in one unit into another equivalent set of units is said to be conversion factor.

Answer to Problem 2ALQ

Total weight of the dimes is equal to $320.6\text{g}$.

Explanation of Solution

Total weight of dimes equals to number of dimes into average weight of a dime ·

Following equation can be used for the calculation.

${\text{n}}_1={\text{y}}_1\times {\text{d}}_1$

Where,

${\text{n}}_1$ represents total weight of dimes

${\text{y}}_1$ represents total number of dimes

${\text{d}}_1$ represents average weight of a dime

Substitute total number of dimes is $140$ and average weight of dime is $2.29\text{g}$

$\begin{array}{l}{\text{n}}_1={\text{x}}_1\times {\text{d}}_1\\ {\text{n}}_1=140\times 2.29\text{g}\\ {\text{n}}_1=320.6\text{g}\end{array}$

Total weight of dimes is equals to $320.6\text{g}$.

Interpretation Introduction

(d)

Interpretation:

Amount of candies that can be bought should be calculated.

Concept Introduction:

An arithmetical multiplier which is used for converting a quantity expressed in one unit into another equivalent set of units is said to be conversion factor.

Answer to Problem 2ALQ

Number of candies that can be bought is $240$ ·

Explanation of Solution

Total sum of pennies and total sum of dimes is the total money which can be spent for candies. Following equation can be used to determine total amount of candies.

${\text{w}}_1=\frac{\left[{\text{x}}_1\times {\text{b}}_1\right]+\left({\text{y}}_1\times {\text{a}}_1\right)}{{\text{k}}_1}\times 4$

Where,

${\text{w}}_1$ represents sum of total candies

${\text{x}}_1$ represents the number of pennies

${\text{b}}_1$ represents the value of a penny

${\text{y}}_1$ represents the number of dimes

${\text{a}}_1$ represents the value of a dime

${\text{k}}_1$ represents value of four candies

Substitute value of a dime is equals to $0·10\text{\$}$ and value of a penny equals to $0·01\text{\$}$ · number of pennies are $210$ and number of dimes are $140$ · Value of four candies is $0·23\text{\$}$

$\begin{array}{l}{\text{w}}_1=\frac{\left[{\text{x}}_1\times {\text{b}}_1\right]+\left({\text{y}}_1\times {\text{a}}_1\right)}{{\text{k}}_1}\times 4\\ {\text{w}}_1=\frac{\left[210\times 0.01\text{\$}\right]+\left(140\times 0.10\text{\$}\right)}{0.23\text{ \$}}\times 4\\ {\text{w}}_1=280\end{array}$

Number of candies can be bought is $280$.

Interpretation Introduction

(e)

Interpretation:

Total weight of candies should be calculated.

Concept Introduction:

An arithmetical multiplier which is used for converting a quantity expressed in one unit into another equivalent set of units is said to be conversion factor.

Answer to Problem 2ALQ

Total weight of the candies is equals to $2864·4\text{g}$ ·

Explanation of Solution

Total weight is the total sum of all candies bought·

Following equation can be used for calculation of total weight.

${\text{W}}_2={\text{W}}_1\times {\text{C}}_1$

Where,

${\text{W}}_2$ represents weight of candies,

${\text{W}}_1$ represents the number of candies

${\text{C}}_1$ represents average weight of candies

Substitute number of candies is $280$ and average weight of candies is $10.23$

$\begin{array}{l}{\text{W}}_2={\text{W}}_1\times {\text{C}}_1\\ {\text{W}}_2=280\times 10.23\text{g}\\ {\text{W}}_2=2864·4\text{g}\end{array}$

Weight of candies is $2864·4\text{g}$.

Interpretation Introduction

(e)

Interpretation:

Number of candies can be bought with twice of dimes should be calculated.

Concept Introduction:

An arithmetical multiplier which is used for converting a quantity expressed in one unit into another equivalent set of units is said to be conversion factor.

Answer to Problem 2ALQ

Number of candies can be bought with twice of dimes is $280$.

Explanation of Solution

Even though dimes twice of dime ( $280$ dimes)is on hand, number of pennies are limited· seller is accepting $3$ pennies with $2$ dimes. Hence, number of candies can be bought is equivalent to amount can be bought with $140$ dimes·

Number of candies can be bought is $280$ ·.