Let the number of madeleines with Jeff be 'j' and the number of madeleines with Bart be 'b'.
Then, if Bart had 57 fewer madeleines than Jeff: \(b = j - 57 …1\)
Given, Bart saved 3/5 of his madeleines.
He must have spent the rest:
\(1\)\(-\)\({3 \over 5}\frac{}{}\)\( = {2\over 5}\frac{}{}\)
Bart's spending =\( {2 \over 5}b\frac{}{}\)
If Jeff spent 2/3 of his madeleines.
He must have saved the rest:
\(1 - \)\( {2 \over 3}={}{}\)\({1 \over 3}\frac{}{}\)
Jeff savings=\( {1 \over 3}\frac{}{}\)
Given: the amount Bart spent was 1/4 of Jeff’s savings.
Thus,
\( {2 \over 5}{}{}\)\(b\)\(=\)\({1 \over 4}{}{} \)\((\)\( {1 \over 3}j{}{}\)\()\)
Cross multiply:
2 * 4 * 3 * b = 1 * 5 * j
24b = 5j ...2
Solve using equation 1 and equation 2:
\(b = j - 57 …1\)
\(24b=5j …2\)
\(24(j-57) = 5j\)
\(24j-1368=5j\)
\(19j=1368\)
\(j = {1368 \over 19}{}^{}=72\)
Hence, Jeff had 72 madeleines originally.
The question is how much did Jeff spend:
Given, Jeff spent 2/3 of the original value: \( {2 \over 3}{}{} * 72 = 48\)
Jeff spent 48 madeleines.
