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 [tex]2x+1.[/tex]
The number of quarters is one half the total number of nickels and dimes, so the number of quarters is [tex]\frac{1}{2}(x+2x+1)=\frac{1}{2}(3x+1)[/tex]
Fill in the table
[tex]\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}[/tex]
Thus, the total sum in cents is
[tex]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[/tex]
The total amount of money in the jar is $1.90 that is 190 cents. So,
[tex]57.5x+17.5=190\\ \\575x+175=1,900\ [\text{Multiplied by 10}]\\ \\575x=1,900-175\\ \\575x=1,725\\ \\x=3[/tex]
Number of dimes = 3
Number of nickels = 7
Number of quarters = 5
Check the total amount of money in the jar:
[tex]3\cdot 10+7\cdot 5+5\cdot 25=30+35+125=190\ cents =\$1.90[/tex]
