Chapter 0.2, Problem 11E

To determine

To calculate:How many of each coin does he have.

Answer to Problem 11E

He has 10 of each coin.

Explanation of Solution

Given information:

The value of a quarter is 25 ¢.

A dime is worth 10¢.

The value of one nickel is 5¢.

Hence, $ 4 is equal to 400 ¢.

Suppose the $x$ is the number of quarters, then $25x$ is the value in cents for all those quarters. Similarly for dimes and nickels (this is an important volatile piece of information, because: $25x+10x+5x=400$

Calculation:

Applythe distribution property, we get

  $\begin{array}{l}25x+10x+5x=400\\ \Rightarrow x\left(25+10+5\right)=400\\ \Rightarrow x\times 40=400\\ \Rightarrow x=\frac{400}{40}\\ \Rightarrow x=10\end{array}$