Question

MONEY Chris has saved twice the number of quarters that Nora saved plus 6. Thenumber of quarters Chris saved is also five times the difference of the number ofquarters and 3 that Nora has saved. Write and solve an equation to find thenumber of quarters they each have saved.

Answer 1

EXPLANATION

Assuming that y represents the savings of Chris and x represent the savings of Nora, we can apply the following relationships:

(1) y= 2x + 6

(2) y = 5(x-3)

Now, we need to match both equations in order to find x:

2x + 6 = 5(x-3)

Applying the distributive property:

2x + 6 = 5x - 15

Subtracting -2x to both sides:

6 = 5x -2x - 15

Adding +15 to both sides:

6 + 15 = 5x - 2x

Adding numbers:

21 = 3x

Dividing both sides by 3:

21/3 = x

Simplifying:

7 = x

Switching sides:

x = 7

Plugging in x=7 into y= 2x + 6:

y = 2*7 + 6

Multiplying and adding terms:

y = 14 + 6

Adding numbers:

y = 20

Hence, the number of quarters they each have saved are:

Chris = 20 quarters

Nora = 7 quarters