Question

every evening jenna empties her pocket and puts pockets and puts her change in a jar. at the end of the week she counts her money. one week she had 50 coins all of them were dimes and quarters. when she added them up she had a total of $10.25 let d=number of dimes and q=numbers of quarters. How many quarters did jenna have?

Answer 1

35 quarters

Explanation:

This problem is a system of equations solving problem.

"one week she had 50 coins all of them were dimes and quarters":

We can write the equation as
`d+q=50`

"when she added them up she had a total of $10.25":

Since value of quarter is 0.25 dollars and dime is 0.10 dollar and total value is 10.25, we can write the equation as
`0.1d+0.25q=10.25`

To solve both of this equation, we can multiply the first equation by -0.1 and then add the 2 equations and solve for q (shown below):

`-0.1(d+q=50)\\\\-0.1d-0.1q=-5\\+0.1d+0.25q=10.25\\-----------\\0.15q=5.25\\q=(5.25)/(0.15)=35`

Hence, Jenna had 35 quarters.

Answer 2

Let x be the number of dimes and y be the number of quarters
You then have the equations, x+y=50 and 0.1x+0.25y=10.25
You can now solve for y.
Solving for y,
x=50-y
0.1(50-y)+0.25y=10.25
5-0.1y+0.25y=10.25
y=35