Answer:
Eli has saved $10
Step-by-step 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 = [tex]\frac{1}{3}[/tex]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 = [tex]\frac{1}{3}[/tex]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 - ( [tex]\frac{1}{3}[/tex]A + 8) = E - E
[tex]\frac{2}{3}[/tex]A - 4 = 0
[tex]\frac{2}{3}[/tex]A = 4
A = 4 × [tex]\frac{3}{2}[/tex] = 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.
Answer:
Eli has saved $10
Step-by-step 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
