Question

Eli and Angela are saving money to buy their grandparents an anniversary gift. Eli has saved 8 more than 1/3 of Angela's savings. If they each save $10 more. Eli will have saved S4 more than Angela's savings. How much has Eli saved?

Answer 1

Answer:

$10

Step-by-step explanation:

Let a = the amount Angela has saved.

Let e = the amount Eli has saved.

"Eli has saved $8 more than 1/3 of Angela's savings."

e = a/3 + 8

"If they each save $10 more." then

Eli will have: e + 10

Angela will have a + 10

"Eli will have saved $4 more than Angela's savings."

e + 10 = a + 10 + 4

This equation simplifies to: e = a + 4

We have a system of two equations in two variables.

e = a/3 + 8

e = a + 4

Since both equations are solved for e, we just equate the right sides.

a/3 + 8 = a + 4

Subtract a/3 from both sides. Subtract 4 from both sides.

a/3 - a/3 + 8 - 4 = a - a/3 + 4 - 4

4 = (2/3)a

Multiply both sides by 3/2

(3/2)4 = (3/2)(2/3)a

6 = a

a = 6

Angela has $6.

e = a + 4 = 6 + 4 = 10

Eli has $10.