Question

Suppose you have x quarters, 3x + 2 dimes, 5x +1 nickels, and 6x + 4 pennies. The value of the coins is $4.59. Write an equation that represents this situation, and find how many of each coin you have. Show your work.

Answer 1

$\text{Suppose you have x quarters, (3x+2) dimes, (5x+1) nickels and (6x+4) pennies}\\ \text{and total value of the coins is }\ 4.59\\ \\ \text{we know that the value of 1 quarter is}=\ 0.25\\ \\ \text{value of 1 dime}=\ 0.10\\ \\ \text{value of 1 Nickel}=\ 0.05\\ \\ \text{value of 1 Penny}=\ 0.01\\ \\ \text{so the equation that represents the given situation is}$

0.25 x+0.10(3x+2)+0.05(5x+1)+0.01(6x+4)=4.59

$\\ \text{now to find the number of each coin, we solve it. so}\\ \\ 0.25 x+0.3x+0.20+0.25x+0.05+0.06x+0.04=4.59\\ \\ 0.86x+0.29=4.59\\ \\ \Rightarrow 0.86x=4.59-0.29\\ \\ \Rightarrow 0.86x=4.3\\ \\ \Rightarrow x=\frac{4.3}{0.86}\\ \\ \Rightarrow x=5$

So the number of quarters is: 5

Number of dimes=3x+2=3(5)+2=17

Number of nickels=5x+1=5(5)+1=26

And number of Pennies=6x+4=6(5)+4=34