Question

hobby store is having a promotion on picture frames: buy 3 get the 4th frame at 75% off.
if f is the cost of one frame, write an expression to represent the total cost for 4 frames in two different ways.
enter the correct answers in the boxes.
show hints
one way:
another way:

Explanation:

Step1: Calculate cost for 3 full - price frames and 1 discounted frame

The cost of 3 full - price frames is $3f$. The 4th frame is at 75% off, so the discount on the 4th frame is 75% of $f$, which is $0.75f$. So the cost of the 4th frame is $f - 0.75f=0.25f$. Then the total cost is $3f + 0.25f$. Combining like terms, we get $3.25f$. Another way to think about the discounted price of the 4th frame is that we pay 25% of $f$ for the 4th frame (since 100% - 75% = 25%), so the cost of the 4th frame is $0.25f$. So total cost is $3f+0.25f = 3.25f$.

Step2: Calculate total cost as 4 times the cost of one frame minus the discount

The original cost of 4 frames without discount is $4f$. The discount on the 4th frame is 75% of $f$, which is $0.75f$. So the total cost is $4f-0.75f$. Combining like terms, we get $3.25f$ as well. Also, we can write the first way as $3f + f(1 - 0.75)$ (since the 4th frame is $f$ minus 75% of $f$) and the second way as $4f-0.75f$.

Answer:

One way: $3f + 0.25f$ (or $3f + f(1 - 0.75)$)
Another way: $4f - 0.75f$