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?
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)
To find the cost of each muffin and how much Ahmad had at first, let's break down the given information step by step:
Step 1: Calculate how much Ahmad had after buying the cupcakes.
- Ahmad spent 1/3 of his money on 12 cupcakes.
- Therefore, he had 2/3 of his money left.
- Let's represent the amount of money he had after buying the cupcakes as x.
Step 2: Calculate how much Ahmad had after buying the muffins.
- Ahmad spent 3/8 of his remaining money on 8 muffins.
- Therefore, he had 5/8 of his money left.
- The amount of money he had after buying the muffins is equal to 5/8 of x.
Step 3: Set up an equation using the given information.
- We know that Ahmad was left with $18 after buying the muffins, so we can write the equation:
(5/8) * x = 18
Step 4: Solve the equation to find the value of x.
- To solve the equation, multiply both sides by 8/5 to isolate x:
x = 18 * (8/5)
x = 28.8
Step 5: Calculate the cost of each muffin.
- Ahmad bought 8 muffins, and the total cost was 3/8 of his remaining money, which is 3/8 * x.
- Divide the total cost by the number of muffins to find the cost per muffin:
Cost of each muffin = (3/8 * x) / 8
Cost of each muffin = (3/8 * 28.8) / 8
Cost of each muffin = 10.8 / 8
Cost of each muffin = $1.35
Step 6: Calculate how much Ahmad had at first.
- Ahmad had x amount of money at first, which we found to be 28.8.
Therefore, the answer to the given problem is:
(a) Each muffin cost $1.35.
(b) Ahmad had $28.8 at first.
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 = ____