Question

In May, Liam and Charlie had the same amount of money in their savings accounts. In June, Liam deposited $140 into his account. Charlie said he increased the money in his account by 5%. When they compared their balances, they found that they were still equal. How much money did they both have in their accounts in May? Enter your answer in the box.

Answer 1

Let's say both had an original amount of "a".

then Liam deposited 140, so it became a + 140.

then Charlie added 5% of "a" to "a", well, 5% of anything is just (5/100)*anything, so 5% of "a" is just (5/100) *a or 0.05a.

then they checked their amounts and both were equal, what the?  let's check.

$\bf \stackrel{\textit{Liam}}{a+140}=\stackrel{\textit{Charlie}}{a+0.05a}\implies a+140=1.05a\implies 140=1.05a-a \\\\\\ 140=0.05a\implies \cfrac{140}{0.05}=a\implies \boxed{2800=a}$