emily saved 25 coins. she saved quarters and one-dollar coins only. if she had a total of $12.25 how many quarters did she have?

Question

I need step by step instructions on how to solve these kinds of problems.

Answer 1

First, identify your variables. Let a be the number of quarters and b the number of one dollar coins.

 

Second, we write down the statement info related to the coins. 

Emily saved 25 coins. This means that the sum of quarters and dollars equals 25.

a + b = 25

 

Total savings equal $12.25

To get this number, you gotta multiply the amount of coins times the value of such coins. That is:

a($0.25) + b($1.00) = $12.25

0.25a + b = 12.25

 

Applying the elimination method, subtract equation 2 from equation 1 and then solve for a (number of quarters).

(a - 0.25a) + (b-b) = (25 - 12.25)

0.75a = 12.75

a = 12.75/0.75

a = 17

 

Solve equation 1 for b (number of dollar coins)

a + b = 25

b = 25 - a

b = 25 - 17

b = 8