Question

Thomas collects dimes and quarters in his change jar. If he has 7 more dimes than quarters, and the total amount of money in the jar is $27.30, find the number of each type of coin in the jar.

Answer 1

Answer:

76 quarters and 83 dimes

Step-by-step explanation:

From the information given, you can write the following equations considering that a quarter represents $0.25 and a dime $0.10:

y=x+7 (1)

0.25x+0.10y=27.30 (2)

x is the number of quarters

y is the number of dimes

Now, you can replace (1) in (2):

0.25x+0.10(x+7)=27.30

0.25x+0.10x+0.7=27.30

0.35x=27.30-0.7

0.35x=26.6

x=26.6/0.35

x=76

Then, you can replace the value of x in (1) to find the value of y:

y=76+7

y=83

According to this, the answer is that there are 76 quarters and 83 dimes in the jar.

Answer 2

There are 76 quarters and 83 dimes in the jar.

Given

Thomas collects dimes and quarters in his change jar.

If he has 7 more dimes than quarters, and the total amount of money in the jar is $27.30.

Let, x be the number of the dimes.

And y be the number of quarters.

If he has 7 more dimes than quarters,

$\rm y=x+7$

The total amount of money in the jar is $27.30.

$\rm 0.25x+0.10y=27.30$

Substitute the value of y in equation 2

$\rm 0.25x+0.10y=27.30\\\\ \rm 0.25x+0.10(x+7) =27.30\\\\ 0.25x + 0.10x + 0.7= 27.30\\\\0.35x=27.30-0.7\\\\0.35x=26.6\\\\x = \dfrac{26.6}{0.35}\\\\\rm x =76$

Substitute the value of x in equation 1

$\rm y = x+7\\\\y =76+7\\\\y=83$

Hence, there are 76 quarters and 83 dimes in the jar.

To know more about Equation click the link given below.

https://brainly.com/question/17555246