Question

Eli has saved $8 more than 1/3 of Angela's savings.If they each save $10 more Eli will have saved &4 more than Angela's savings.How much has Eli saved?

Answer 1

Eli has saved $10

Explanation:

Let us denote Angela's saving by "x".

If Eli's saving is $8 more than one-third of Angela's saving, then Eli's saving is:

[(1/3 × x) + 8 = x/3 + 8]

We will make x/3 + 8 to have a common denominator:

x/3 + 8 = (x+24)/3

If Eli and Angela each saved $10 more, then their respective savings would have been:

(x+24)/3 + 10 for Eli

x+10 for Angela.

At this savings, Eli would have been $4 richer than Angela.

i.e [((x + 24)/3) + 10] - (x+10) = $4

We will make [(x+24)/3] + 10 to have common denominator.

(x + 24 + 30)/3

= (x + 54)/3

Then:

[(x+54)/3] - [(x+10)/1] = 4

[x+54-(3x+30)]/3 = 4/1

(-2x + 24)/3 = 4

cross multiply

-2x + 24 = 12

-2x = -12

x = -12/-2

x = 6

Since Eli's saving = x/3 + 8

Then his actual saving

= 6/3 + 8

= 2 + 8

= $10

Answer 2

Eli has saved $10

Explanation:

Let us use the first letters of their names to represent them.

A for Angela and E for ELi

So, from the first statement, we can write out an equation: E =
`(1)/(3)`A + 8, that is, one-third of Angela's savings + $8 will give us Eli's savings

From the second statement, we can write out: E + 10 = (A + 10) + 4 which means that if $10 is added to both their savings, Eli will still have $4 more than Angela.

So, we can solve both equations;

Equation 1: E =
`(1)/(3)`A + 8

Equation 2: E + 10 = (A + 10) + 4; which can be rewritten as E + 10 = A + 14

and then E = A + 4

The two equations (in bold), can then be solved simultaneously.

Let us carry out this operation to eliminate the E: Subtract equation 1 from equation 2, so that;

A + 4 - (
`(1)/(3)`A + 8) = E - E

`(2)/(3)`A - 4 = 0

`(2)/(3)`A = 4

A = 4 ×
`(3)/(2)` = 6

So, if A is 6, and E = A + 4 (from equation 2, that means that E = 6 + 4 = 10

So, Eli has saved $10, while Angela has saved $6.

If we check what was said in the question about their savings, which is what we have represented using the equations, the answers can be confirmed.