Math worksheet with word problems on markups and markdowns for independent practice.

Let's solve each problem step by step and explain the reasoning.

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1) A painting is on sale at 50% off. The sale price is $320. What was the original price?

Explanation:
If the painting is 50% off, then the sale price is 50% of the original price.

Let the original price be $ x $.
So:
$$
0.5x = 320
$$
Divide both sides by 0.5:
$$
x = \frac{320}{0.5} = 640
$$

✔ Answer: $640

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2) Fred buys a video game disk for $4. There was a discount of 20%. What is the sales price?

Wait! This says "Fred buys... for $4" — that seems to be the sale price, but it asks for the sales price again?

Let’s re-read: “Fred buys a video game disk for $4. There was a discount of 20%.” So $4 is the sale price, and we are told there was a 20% discount.

But the question asks: *What is the sales price?* That would just be $4.

But that doesn’t make sense — maybe it’s asking for the original price before discount?

Alternatively, perhaps the $4 is the original price, and we need to find the sale price after 20% discount.

Let’s assume the original price is $4, and it’s discounted by 20%.

Then:
$$
\text{Discount amount} = 0.20 \times 4 = 0.80
$$
$$
\text{Sale price} = 4 - 0.80 = 3.20
$$

✔ Answer: $3.20

> ✔ But if the $4 is already the sale price, then the question is confusing. Based on typical wording, likely the original price is $4, so sale price is $3.20.

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3) A boat is marked up 20% on the original price. The original price was $50. What is the sale price of the boat before sales tax?

Explanation:
A 20% markup means the sale price is 120% of the original.

$$
\text{Sale price} = 50 + (0.20 \times 50) = 50 + 10 = 60
$$

Or:
$$
1.20 \times 50 = 60
$$

✔ Answer: $60

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4) A football is selling for 35% off the original price. The original price was $60. What is the sale price of the football?

Explanation:
35% off means you pay 65% of the original price.

$$
\text{Sale price} = 60 \times (1 - 0.35) = 60 \times 0.65 = 39
$$

✔ Answer: $39

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5) Timmy wants to buy a scooter and the price was $50. When he goes to the store a second time, he found that price was marked down by 20%. What is the new price?

Explanation:
20% off $50:

$$
\text{Discount} = 0.20 \times 50 = 10
$$
$$
\text{New price} = 50 - 10 = 40
$$

✔ Answer: $40

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6) Andrew paid $10 for a burger. The burgers went on sale and there was a discount of 20%. What was the sale price of the burgers?

This is tricky. He paid $10, which is after the 20% discount.

So $10 is the sale price, meaning the original price was higher.

Let original price = $ x $

After 20% discount:
$$
0.80x = 10
$$
$$
x = \frac{10}{0.80} = 12.50
$$

But the question asks: *What was the sale price?*

He paid $10, so sale price is $10.

But that seems too simple.

Wait — the wording is: “Andrew paid $10 for a burger. The burgers went on sale and there was a discount of 20%.”

So the sale price is $10.

But maybe it’s asking what the original price was?

But it clearly says: “What was the sale price?”

So sale price = $10

✔ Answer: $10

> But this feels like a trick. Alternatively, maybe the $10 is the original price, and he got a 20% discount.

But the sentence says: “Andrew paid $10” — so that must be the sale price.

So yes: $10

✔ Answer: $10

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7) Emily buys a toaster during the sale for 10% off. If Ellen pays $36, what was the original price?

Assuming “Ellen” is a typo and should be “Emily”.

She paid $36 after 10% discount → $36 is 90% of the original price.

Let original price = $ x $

$$
0.90x = 36
$$
$$
x = \frac{36}{0.90} = 40
$$

✔ Answer: $40

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8) Zack has an old car. He wants to sell it for 60% off the current price. The market price is $500. How much money would he receive in exchange for the car if he were able to sell it at that rate?

“60% off the current price” → so he sells it for 40% of $500.

$$
\text{Selling price} = 500 \times (1 - 0.60) = 500 \times 0.40 = 200
$$

✔ Answer: $200

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9) Drew bought a chemistry book for $30. Later that book was marked down by 20%. By how much has the value been decreased?

Original price = $30
Marked down by 20% → decrease = 20% of $30

$$
\text{Decrease} = 0.20 \times 30 = 6
$$

So the value decreased by $6.

✔ Answer: $6

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10) What is the original price if there is a 10% discount and the sale price is $76.50?

Sale price = 90% of original price

Let original price = $ x $

$$
0.90x = 76.50
$$
$$
x = \frac{76.50}{0.90} = 85
$$

✔ Answer: $85

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## ✔ Final Answers:

1) $640
2) $3.20 (assuming $4 is original price)
3) $60
4) $39
5) $40
6) $10
7) $40
8) $200
9) $6
10) $85

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