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TACHS Math : Word problems

Study concepts, example questions & explanations for TACHS Math

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Example Questions

Example Question #1 : Solving One Step Problems

Tim can ride his bike eight miles in one hour. How long will it take him to ride forty miles?

Possible Answers:

$10\textup{ hours}$

$15\textup{ hours}$

Cannot be determined

$4\textup{ hours}$

$5\textup{ hours}$

Correct answer:

$5\textup{ hours}$

Explanation:

If Tim can ride his bike eight miles in one hour then we can write the following ratio:

$\frac{8\textup{ miles}}{1\textup{ hour}}$

Next, we want to know how long it will take him to ride forty miles. We can write the following ratio:

$\frac{40\textup{ miles}}{x\textup{ hours}}$

Next, we can set these equal to one another and form a proportion.

$\frac{8\textup{ miles}}{1\textup{ hour}}=\frac{40\textup{ miles}}{x\textup{ hours}}$

Cross multiply and solve for the variable.

$\frac{8\textup{ miles}}{1\textup{ hour}}\times\frac{40\textup{ miles}}{x\textup{ hours}}$

Simplify.

$8\times x=40\times1$

8x=40

Divide each side of the equation by .

$\frac{8x}{8}=\frac{40}{8}$

Solve.

$x=5\textup{ hours}$

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Example Question #2 : Word Problems

Barry, Jerry, and Mary order a pizza. Barry pays half the cost; Jerry pays one third of the cost; Mary pays the rest, which is $3. How much did the pizza cost?

Possible Answers:

$\$ 20$

$\$15$

$\$18$

$\$21$

Correct answer:

$\$18$

Explanation:

Let be the cost of the pizza. Barry paid half the cost of the pizza, which is $\frac{1}{2}C$ ; Jerry paid one third of the cost, which is $\frac{1}{3}C$ , and Mary paid $3. The sum of their shares of the cost is equal to the total cost, so the equation to set up is

$C =\frac{1}{2}C+ \frac{1}{3}C + 3$

Solve for by isolating the variable at left. First, at right, collect the like terms by adding the coefficients of . This requires finding the least common denominator of the two fractions, which is 6:

$C =\frac{1 \cdot 3}{2 \cdot 3}C+ \frac{1 \cdot 2}{3 \cdot 2}C + 3$

$C =\frac{ 3}{6}C+ \frac{2}{6}C + 3$

$C =\left (\frac{ 3}{6} + \frac{2}{6} \right )C + 3$

$C = \frac{5}{6} C + 3$

Subtract $\frac{5}{6} C$ from both sides, again by collecting like terms:

$C - \frac{5}{6}C = \frac{5}{6} C + 3 - \frac{5}{6}C$

$\frac{6}{6} C - \frac{5}{6}C = 3$

$\left (\frac{6}{6} - \frac{5}{6} \right )C = 3$

$\frac{1}{6} C = 3$

Now multiply both sides by 6 to reverse multiplication by $\frac{1}{6}$ :

$6\cdot \frac{1}{6} C =6 \cdot 3$

C = 18

The pizza cost $18.

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Example Question #1 : Solving Multi Step Problems

The first 60 miles of a 100-mile trip took one hour; the whole trip took two hours and fifteen minutes. To the nearest whole, what was the average speed during the remaining 40 miles of the trip?

Possible Answers:

40 miles per hour

32 miles per hour

36 miles per hour

50 miles per hour

Correct answer:

32 miles per hour

Explanation:

The average speed during a trip of miles over a period of hours is $\frac{d}{t}$ miles per hour. Here, the distance driven is 40 miles; the time it took was two hours and fifteen minutes total minus the hour for the first 40 miles, which is one hour and fifteen minutes. Since fifteen minutes is equal to

$\frac{15 \div 15 }{60 \div 15} = \frac{1}{4}$ hours, we get

d= 40 and $t = 1\frac{1}{4}$

Therefore, the average speed traveled during the second part of the trip is

$\frac{40}{1\frac{1}{4}}$

$= 40 \div 1\frac{1}{4}$

$= 40 \div \frac{5}{4}$

$= \frac{40}{1} \times \frac{4}{5}$

$= \frac{8}{1} \times \frac{4}{1}$

= 32 miles per hour.

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Example Question #1 : Word Problems

Jeremy has pieces of candy. Maggie has half as many pieces of candy as Jeremy has, and Harold has twice as many pieces of candy as Jeremy and Maggie combined. How many pieces of candy does Harold have?

Possible Answers:

Correct answer:

Explanation:

Start by finding how many pieces of candy Maggie has. Since she has half as many as Jeremy, she must have pieces. Then, Jeremy and Maggie have pieces of candy together. Since Harold has twice as many as the two of them together, Harold must have pieces of candy.

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Example Question #41 : Math

Taylor is years old. Her father is three times her age. Her mother is two years older than her father. What is the sum of the ages of Taylor, her father, and her mother?

Possible Answers:

105

107

109

111

Correct answer:

107

Explanation:

Start by multiplying Taylor's age by to find her father's age.

$15\times 3 =45$

Her father must be years old. Since her mother is two years older than her father, her mother must be years old.

Now, add up all their ages to find the sum of their ages.

15+45+47=107

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Example Question #41 : Math

When Steve started his diet, he weighed 240 pounds. After the first month, he lost $\frac{1}{12}$ of his weight. In his second month, he lost $10\%$ of the remaining weight. How many pounds does Steve weigh now?

Possible Answers:

200

198

196

194

Correct answer:

198

Explanation:

Start by finding how much weight Steve lost after the first month. Since he lost $\frac{1}{12}$ of his starting weight of 240 , he must have lost pounds.

This means that at the end of his first month, he weighed 220 pounds.

Since he lost $10\%$ of his remaining weight in the second month, he must have lost pounds from his 220 pounds.

Thus, Steve must weigh 198 pounds now.

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Example Question #3 : Word Problems

A school library uses shelves that can hold 325 books. If they have shelves that are completely full and one shelf that is only $80\%$ full, how many books does the library have?

Possible Answers:

6660

6820

6520

6760

Correct answer:

6760

Explanation:

Start by finding out how many books the full shelves can hold by multiplying it by the number of books held per shelf.

$20\times 325=6500$

Next, find out how many books are held by the shelf that is not completely full.

$325 \times 0.8=260$

Now, add the two together to find how many books total are in the library.

6500+260=6760

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TACHS Math : Word problems

Study concepts, example questions & explanations for TACHS Math

All TACHS Math Resources

Example Questions

Example Question #1 : Solving One Step Problems

Example Question #2 : Word Problems

Example Question #1 : Solving Multi Step Problems

Example Question #1 : Word Problems

Example Question #41 : Math

Example Question #41 : Math

Example Question #3 : Word Problems

All TACHS Math Resources

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