Question

Ahmad had a sum of money at first. He spent 1/3 of his money on 12
cupcakes and 3/8 of his remaining money on 8 muffins. He was then
left with $18.

(a) How much did each muffin cost?
(b) How much did he have at first?

Answer 1

spent 1/3, leaving 2/3
spent 3/8 * 2/3 = 1/4, leaving 2/3 - 1/4 = 5/12
so,
(b) 5/12 x = 18
solve for x, then
(a) 1/8 * 1/4 x = ____

Answer 2

initially, Ahmad has x dollars
1/3x dollars spent on 12 cupcakes
3/8 (x - 1/3x) dollars spent on 8 muffins now he has $18


x - 1/3x - 3/8(x - 1/3x) = 18
x - 1/3x - 3/8 (2/3x) = 18
x - 1/3x - 1/4x = 18
multiply both sides by 12
12 (x - 1/3x - 1/4x) = 12 • 18
12x - 4x - 3x = 216
5x = 216
x = 216/5
x = 43.2
he has initially $43.2 answer (b)



y = 3/8 (x - 1/3x) dollars spent on 8 muffins.

y = 3/8 (x - 1/3x)
y = 3/8 (2/3x)
y = 1/4x
take x=43.2
y = 1/4 • 43.2
y = 10.8
$10.8 spent on 8 muffins

so the cost of each muffin is
C = y/8
C = 10.8/8
C = 13.5
the cost of each muffin is $1.35 answer (a)