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Multistep Ratio and Percent Problems

Grade 7·Common Core Math - Grade 7·standard·7-rp-a-3

Work through problems with immediate feedback

Recall / Warm-Up

Which of the following correctly expresses $35\%$ as a decimal?

$3.5$

$0.35$

$0.035$

$35$

What is $20\%$ of $65$ ?

$3.25$

$130$

$13.00$

$1.30$

A shirt originally costs $120$ . The store is offering $25\%$ off. What is the discount amount in dollars?

Fluency Practice

A meal costs $24.00$ . Sales tax is $8.5\%$ . What is the total cost including tax? Round to the nearest cent.

A sweater originally costs $45$ . It is on sale for $30\%$ off. What is the sale price?

A salesperson earns $6\%$ commission on $2{,}500$ in merchandise sales. How much commission does she earn?

A bank account has a principal of $600$ at $4\%$ annual simple interest. Using $I = prt$ : the interest earned after $3$ years is $ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ . The total balance after $3$ years is $ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ .

interest earned:

total balance:

A store buys a blender wholesale for $50$ and marks it up by $40\%$ . What is the retail price?

$20$

$70$

$90$

$57$

Varied Practice

A price drops from $80$ to $64$ . Which expression correctly computes the percent decrease?

$\dfrac{16}{80} \times 100$

$\dfrac{16}{64} \times 100$

$\dfrac{64}{80} \times 100$

$\dfrac{80 - 64}{100}$

A savings account has a principal of $800$ at $3.5\%$ annual simple interest. Using $I = prt$ , fill in: $I$ = ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ $\times$ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ $\times t$ . The interest earned after $4$ years is $ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ .

p (principal):

r (rate as decimal):

interest after 4 years:

A student measures a table as $58$ inches long. The actual length is $60$ inches. Which expression gives the percent error?

$\dfrac{|58 - 60|}{60} \times 100$

$\dfrac{|58 - 60|}{58} \times 100$

$\dfrac{60 - 58}{58} \times 100$

$\dfrac{58 - 60}{60} \times 100$

A town's population of $4{,}800$ increases by $12.5\%$ . What is the new population?

Word Problems

A customer at a restaurant orders a meal that costs $35.00$ . The sales tax rate is $7\%$ . The customer decides to leave an $18\%$ tip based on the pre-tax meal cost.

What is the tax amount on the meal? Round to the nearest cent.

What is the total amount the customer pays (meal + tax + tip)? Round to the nearest cent.

A winter jacket was originally priced at $180$ . During a clearance sale, it is now priced at $135$ .

What is the percent decrease in price? Express as a whole number percent.

During a science lab, a student measures a room's width as $18$ feet. The actual width of the room is $15$ feet.

What is the percent error of the student's measurement? Express as a whole number percent.

An investor places a principal of $1{,}200$ in a savings account that earns $5\%$ annual simple interest.

How many years will it take to earn $300$ in interest? Use $I = prt$ and solve for $t$ .

Error Analysis

$Two-column contrast card. Left (yellow): wrong thinking assumes +25% and -25% cancel, leaving $100. Right (teal): correct steps show $100 × 1.25 = $125, then $125 × 0.75 = $93.75, because the second percent applies to the new value.$

A $100$ item increases in price by $25\%$ , then later decreases in price by $25\%$ .

Marcus claims: 'The final price is $100$ because a $25\%$ increase and a $25\%$ decrease cancel each other out.'

What error did Marcus make?

Marcus added the percents instead of multiplying the scale factors — the correct answer is $93.75$ , not $100$ .

Marcus used the wrong percent — the increase should be $20\%$ to cancel a $25\%$ decrease.

Marcus forgot to apply the tax — the final price would be higher than $100$ after tax.

Marcus's reasoning is correct — the two changes do cancel, and the final price is $100$ .

A store's revenue increased from $4{,}000$ to $4{,}600$ .

Omar computes the percent increase:
$\text{Percent increase} = \frac{600}{4{,}600} \times 100 \approx 13\%$

What error did Omar make?

Omar used the new value ( $4{,}600$ ) as the denominator instead of the original value ( $4{,}000$ ).

Omar computed the wrong change — the change should be $4{,}600 - 4{,}000 = 700$ , not $600$ .

Omar should have multiplied by 1,000 instead of 100 to convert to percent.

Omar should have divided by the average of $4{,}000$ and $4{,}600$ .

Challenge

A car dealer purchases a car at a wholesale price of $18{,}000$ . The dealer marks the price up by $22\%$ . A buyer purchases the car and must also pay $7.5\%$ sales tax on the marked-up price. What is the total purchase price the buyer pays?

Two savings account options both start with a principal of $1{,}000$ :

Option A: $4\%$ annual simple interest for $5$ years
Option B: $6\%$ annual simple interest for $3$ years

Compute the interest earned by each option. Explain which option earns more interest and why, even though Option B has a higher interest rate.

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