Im having trouble with my homework If anyone can help I will appreciate it so much

Question

Sierra has a total of 61 dimes and quarters in her piggybank. She has 3 more
quarters than dimes. The coins have a total value of $10.90. How many dimes and
how many quarters does she have?

Answer 1

Let # of dimes = x

Let # of quarters = x + 3

 

Using these variables, we can write an equation that represents the total amount in dollars and equation that represents the total number of coins.

 

 

x + (x + 3) = 61                                 eq1     ------>  total number of coins

 

0.10x + 0.25(x + 3) = 10.90               eq2      ------>  total amount in dollars

 

 

We now have a system of equation.

 

 

If we take eq1, we can solve for the term (x + 3).

 

x + 3 = 61 - x

 

 

Next, we can substitute this value of (x + 3) into eq2.  We get

 

0.10x + 0.25(61 - x) = 10.90

 

 

This bolded equation is what you need to solve for x for.

Answer 2

61 - 3 (3 more quarters) = 58 / 2 = 29

 

29 dimes x .10 = $2.90

 

32 quarters x .25 = $8.00

 

total $10.90