Katie made some chocolate truffles. Katie gave 1⁄4 of her truffles to Leanne. Then Katie gave 1⁄2 of the remaining truffles to Jeff. At that point, Katie had 18 truffles left. How many chocolate truffles did Katie have at first?
Never heard of a subject called Tupper.
anyhow....
let the number of Katies truffles be x
after first gifting:
Katie had (3/4)x left
she gave 1/2 of those away leaving her with
(1/2)(3/4)x or (3/8)x truffles
(3/8)x = 18
3x = 144
x = 48
So she started with 48
check:
she gave 1/4 away or 12, so she is left with 36
she then gave half of those away, leaving her with 18
all checks out.
"Tupper" is a school subject I have not heard of.
Let's solve the problem step by step:
Step 1: Katie gave 1/4 of her truffles to Leanne. This means she had 3/4 of her truffles remaining.
Step 2: Katie gave 1/2 of the remaining truffles to Jeff. This means she had 1/2 * 3/4 = 3/8 of her truffles remaining.
Step 3: Katie had 18 truffles left. We can set up an equation to represent this:
3/8 * x = 18
where x is the number of truffles Katie had at first.
Step 4: To solve the equation, we need to isolate x. We can do this by multiplying both sides of the equation by the reciprocal of 3/8, which is 8/3.
(3/8 * x) * (8/3) = 18 * (8/3)
x = 144/3
x = 48
Therefore, Katie had 48 chocolate truffles at first.
To find out how many chocolate truffles Katie had at first, we can work backwards from the given information.
Let's call the number of truffles Katie had initially "x."
Katie gave 1/4 of her truffles to Leanne, which means she had 3/4 of the truffles left. So we can write this as:
(3/4) * x
Next, Katie gave 1/2 of the remaining truffles to Jeff. After giving truffles to Jeff, she had 18 truffles left. So we can write this as:
(1/2) * (3/4) * x = 18
To solve this equation, we need to isolate x, so let's simplify the expression:
(1/2) * (3/4) * x = 18
Multiply the fractions:
(3/8) * x = 18
To isolate x, divide both sides of the equation by (3/8):
x = 18 / (3/8)
To divide by a fraction, multiply by its reciprocal:
x = 18 * (8/3)
x = 48
Therefore, Katie initially had 48 chocolate truffles.