Multi-Step Ratio and Percent Problems - 7th Grade Math

1. Find the tip on a $40 bill at $15\%$.

   $6. Calculate $40 \times 0.15 = 6$.

2. A store marks up $40 by $15\%$. What is the new price?

   $46. Calculate $40 \times 1.15 = 46$.

3. State the formula for percent error when experimental is $E$ and accepted is $A$.

   $\frac{|E-A|}{A}\times 100\%$. Absolute difference over accepted value, times $100\%$.

4. What is the sale price of $60 after a $25\%$ discount?

   $45. Calculate $60 \times (1 - 0.25) = 60 \times 0.75$.

5. State the percent change formula using change and original value.

   $\%\text{ change} = \frac{\text{change}}{\text{original}}\times 100\%$. Divide the change by original, then multiply by 100%.

6. State the formula for tip amount when bill is $b$ and tip rate is $r$ (decimal).

   $\text{tip} = br$. Tip equals bill amount times tip rate (as decimal).

7. What decimal is equivalent to $7\%$?

   $0.07$. Move decimal point two places left: 7% = 0.07.

8. Find the tip on a $\30$ meal at $20\%$.

   $\6$. Calculate $30 \times 0.20 = 6$.

9. What is the total balance formula $A$ after simple interest $I$ is added to principal $P$?

   $A = P + I$. Total amount is principal plus interest earned.

10. State the formula for price after a markup rate $m$ on original cost $c$.

    $\text{new price} = c(1+m)$. Multiply cost by $(1 + \text{markup rate})$.

11. State the formula for simple interest when principal is $P$, rate is $r$, and time is $t$.

    $I = Prt$. Interest equals principal times rate times time.

12. State the formula for tip amount when bill is $b$ and tip rate is $t$.

    $\text{tip} = bt$. Tip equals bill times tip rate.

13. What is the total cost after $7.5\%$ tax is added to $80?

    $86. Add tax to original: $80 + 6 = 86$.

14. State the formula for sale price after a discount rate $d$ on original price $p$.

    $\text{sale price} = p(1-d)$. Multiply price by $(1 - \text{discount rate})$.

15. State the formula for commission earned when sales are $s$ and commission rate is $r$ (decimal).

    $\text{commission} = sr$. Commission is sales times commission rate (as decimal).

16. Find the tax on $80 at a tax rate of $7.5\%$.

    $6. Tax is $80 \times 0.075 = 6$.

17. Find the percent increase from $50$ to $65$.

    $30\%$. Change is $15$, so $\frac{15}{50} \times 100\% = 30\%$.

18. What is $15\%$ of $80$?

    $12$. Convert 15% to 0.15, then multiply: $0.15 \times 80 = 12$.

19. State the formula for tax amount when price is $p$ and tax rate is $r$ (decimal).

    $\text{tax} = pr$. Tax amount is price times tax rate (as decimal).

20. State the formula for commission earned when sales are $s$ and commission rate is $r$.

    $\text{commission} = sr$. Commission equals sales times commission rate.

21. A salesperson earns $6\%$ commission on $500 in sales. What is the commission?

    $30. Calculate $500 \times 0.06 = 30$.

22. State the formula for simple interest $I$ when principal is $P$, rate is $r$, and time is $t$.

    $I = Prt$. Simple interest equals principal times rate times time.

23. State the percent error formula using measured value and accepted value.

    $\%\text{ error} = \frac{|m-a|}{a}\times 100\%$. Use absolute difference over accepted value, times 100%.

24. State the formula for sale price after a markdown of rate $r$ (decimal) on original price $p$.

    $\text{sale price} = p(1-r)$. Sale price is original times (1 minus markdown rate).

25. State the formula for total amount after simple interest using $P$ and interest $I$.

    $A = P + I$. Total amount is principal plus interest earned.

26. State the formula for total price with tax when price is $p$ and tax rate is $r$ (decimal).

    $\text{total} = p(1+r)$. Total with tax is price times (1 + tax rate).

27. A price rises from $40 to $50. What is the percent increase?

    $25\%$. Calculate $\frac{50-40}{40} \times 100\% = \frac{10}{40} \times 100\%$.

28. What is $18\%$ of $50$?

    $9$. Multiply $50 \times 0.18 = 9$.

29. Find the percent error when measured is $52$ and accepted is $50$.

    $4\%$. Error is $\frac{|52-50|}{50} \times 100\% = \frac{2}{50} \times 100\% = 4\%$.

30. A $50 bill includes a $10\%$ tip. What was the pre-tip bill amount?

    $\frac{\$50}{1.10}$. Divide total by $1.10$ to find original bill.

31. State the formula for markup amount when cost is $c$ and markup rate is $r$ (decimal).

    $\text{markup} = cr$. Markup amount is cost times markup rate (as decimal).

32. Find the sale price of a $120 item after a $30\%$ markdown.

    $84. Calculate $120 \times (1 - 0.30) = 120 \times 0.70 = 84$.

33. What percent is equivalent to the decimal $0.35$?

    $35\%$. Move decimal point two places right: 0.35 = 35%.

34. A value drops from $80$ to $60$. What is the percent decrease?

    $25\%$. Calculate $\frac{80-60}{80} \times 100\% = \frac{20}{80} \times 100\%$.

35. Find the commission on $600 in sales at $5\%$.

    $30. Calculate $600 \times 0.05 = 30$.

36. Find the total cost of a $50 item with $8\%$ sales tax.

    $54. Calculate $50 \times 1.08 = 54$.

37. Find the selling price if an item costs $80 and is marked up $25\%$.

    $100. Selling price is $80 + (80 \times 0.25) = 80 + 20 = 100$.

38. Identify the decimal form of $35\%$.

    $0.35$. Move decimal point two places left to convert percent to decimal.

39. Find the percent error when $E=52$ and $A=50$.

    $4\%$. Calculate $\frac{|52-50|}{50} \times 100\% = \frac{2}{50} \times 100\%$.

40. State the formula for percent change from original $o$ to new $n$.

    $\frac{n-o}{o}\times 100\%$. Subtract original from new, divide by original, multiply by $100\%$.

Study these flashcards