Question

A change jar contains nickels, dimes and quarters. The total amount of money in the jar is $1.90. The amount of nickels is one more than twice the number of dimes. The number of quarters is one half the total number of nickels and dimes. Find the number of each coin in the change jar.

Answer 1

Answer:

Number of dimes = 3

Number of nickels = 7

Number of quarters = 5

Step-by-step explanation:

Let x be the number of dimes in the jar.

The amount of nickels is one more than twice the number of dimes, then the amount of nickels is $2x+1.$

The number of quarters is one half the total number of nickels and dimes, so the number of quarters is $\frac{1}{2}(x+2x+1)=\frac{1}{2}(3x+1)$

Fill in the table

$\begin{array}{ccc}&\text{Number of coins}&\text{Value in these coins in cents}\\ \\\text{Dimes}&x&10x\\\text{Nickels}&2x+1&5(2x+1)\\\text{Quarters}&\frac{1}{2}(3x+1)&25\cdot \frac{1}{2}(3x+1)\end{array}$

Thus, the total sum in cents is

$10x+5(2x+1)+\dfrac{25}{2}(3x+1)\\ \\=10x+10x+5+\dfrac{75}{2}x+\dfrac{25}{2}\\ \\=20x+37.5x+5+12.5\\ \\=57.5x+17.5$

The total amount of money in the jar is $1.90 that is 190 cents. So,

$57.5x+17.5=190\\ \\575x+175=1,900\ [\text{Multiplied by 10}]\\ \\575x=1,900-175\\ \\575x=1,725\\ \\x=3$

Number of dimes = 3

Number of nickels = 7

Number of quarters = 5

Check the total amount of money in the jar:

$3\cdot 10+7\cdot 5+5\cdot 25=30+35+125=190\ cents =\ 1.90$