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High School Math : How to do word problems where one quantity is unknown

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Example Questions

Example Question #11 : How To Do Word Problems Where One Quantity Is Unknown

What percent of is ?

Possible Answers:

$12.5\%$

$7.5\%$

$15\%$

$20\%$

$10\%$

Correct answer:

$20\%$

Explanation:

Look for the verbal cues in the question. IS represents "equals" and OF represents multiplication.

Then the equation to solve becomes:

$P\cdot 75=15$ so P=0.20 or $20\%$

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Example Question #12 : How To Do Word Problems Where One Quantity Is Unknown

Joy earns a $5\%$ commission on each house she sells. How much money does she make when she sells two houses for $\$69,000$ each and another house for $\$75,000$ ?

Possible Answers:

$\$11,500$

$\$7,850$

$\$8,750$

$\$9,925$

$\$10,650$

Correct answer:

$\$10,650$

Explanation:

In general, a commission problem has the form:

$\$\; sales \cdot \%\; commission = \$ \; commission$

$Total \; sales= 69,000+69,000+75,000=\$213,000$

So the commission is:

$213,000\cdot 0.05=\$10,650$

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Example Question #11 : How To Do Word Problems Where One Quantity Is Unknown

Edward is making cookies. The full recipe makes 144 cookies. He decides to cut the recipe by four. How many dozens of cookies will he make?

Possible Answers:

Correct answer:

Explanation:

Cut the recipe by four: $144\div 4=36$ cookies; however, the question asks for how many DOZENS of cookies are made, so the correct answer is dozen cookies.

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Example Question #14 : Algebraic Equations

Dean is counting his money. He has five more quarters than nickles and four less nickles than dimes. He has $\$2.85$ . How many coins does he have?

Possible Answers:

Correct answer:

Explanation:

Money problems generally consist of two parts: total number of coins and total value of money.

Let number of nickles, x+5= number of quarters, and x+4= number of dimes.

So the equation to solve becomes:

0.05x+0.25(x+5)+0.10(x+4)= 2.85 or

0.05x+0.25x+1.25+0.10x+0.40=2.85 so

0.40x=1.20

Thus, x = 3 , so there are three nickles, eight quarters and seven dimes for a total of coins.

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Example Question #12 : How To Do Word Problems Where One Quantity Is Unknown

Golden Sunshine paint is made by mixing one part red paint and three parts yellow paint. How many gallons of yellow paint should be mixed with three quarts of red paint?

Possible Answers:

$1.50\; gallons$

$1.75\; gallons$

$2.50\; gallons$

$2.25\; gallons$

$2.75\; gallons$

Correct answer:

$2.25\; gallons$

Explanation:

Use proportions to solve this problem.

Let quarts of yellow paint.

$\frac{3\; yellow}{1\; red}= \frac{x\; qt \; yellow\; paint}{3\; qt \; red\; paint}$

By cross-multiplying we get $x = 9\; qt \; yellow\; paint$ .

Since $4 \; quarts = 1\; gallon$ , we actually need $2.25\; gallons \; yellow\; paint$ .

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Example Question #12 : How To Do Word Problems Where One Quantity Is Unknown

If $1\; in=2.54\; cm$ , approximately how many meters are in $24 \; ft$ ?

Possible Answers:

$7.9\; m$

$7.2\; m$

$8.4\; m$

$6.8\; m$

$8.1\; m$

Correct answer:

$7.2\; m$

Explanation:

Use the factor-label method to solve this problem:

$24 \; ft\cdot \frac{12\; in}{1\; ft}\cdot \frac{2.5\; cm}{1\; in}\cdot \frac{1\; m}{100\; cm}=7.2\; m$

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Example Question #14 : How To Do Word Problems Where One Quantity Is Unknown

The length of a rectangle is ten more than the width. The perimeter is $80\; ft$ . What is the area of the rectangle?

Possible Answers:

$300\; ft^{2}$

$225\; ft^{2}$

$350\; ft^{2}$

$375\; ft^{2}$

$425\; ft^{2}$

Correct answer:

$375\; ft^{2}$

Explanation:

For a rectangle:

P=2w+2l and $A=w\cdot l$

Let width and x+10 = length.

Thus P=2x+2(x+10)=80 , so the width is $15\; ft$ and the length is $25\; ft$ .

Then the area becomes $A= w\cdot l=15\cdot 25=375 \; ft^{2}$ .

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Example Question #15 : How To Do Word Problems Where One Quantity Is Unknown

Let $1\; gallon=3.79\; L$ . If gasoline sells for $\$3.10$ per gallon, approximately how much would $2.5\; L$ cost?

Possible Answers:

$\$2.50$

$\$2.00$

$\$1.75$

$\$1.50$

$\$2.25$

Correct answer:

$\$2.00$

Explanation:

Use the factor-label nethod to solve this problem:

$2.5\; L\cdot \frac{1\; gallon}{3.79\; L}\cdot \frac{\$3.10}{1\; gallon}=\$2.04$ or approximately $\$2.00$ .

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Example Question #16 : How To Do Word Problems Where One Quantity Is Unknown

Two brothers are dividing up the family farm to make work easier. Frank and George divide 160 acres in a ratio of $3\; to\; 5$ . How many acres will George work?

Possible Answers:

$80\; acres$

$100\; acres$

$50\; acres$

$120\; acres$

$60\; acres$

Correct answer:

$100\; acres$

Explanation:

Use proportions to solve this problem:

Let acres worked by Frank and 160-x= acres worked by George.

$\frac{Frank}{George}= \frac{3}{5}=\frac{x}{160-x}$

Cross-multiply to get 3(160-x)=5x or 480-3x=5x so x=60 .

So Frank works $60\; acres$ and George works $100 \; acres$ .

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Example Question #17 : How To Do Word Problems Where One Quantity Is Unknown

According to Newton's laws of Motion, force equals mass times acceleration, or F=ma . If a $3\; kg$ mass exerts a force of $45\; Newtons$ , what force would a $12\; kg$ mass exert at he same acceleration?

Possible Answers:

$210 \; Newtons$

$150 \; Newtons$

$275 \; Newtons$

$240 \; Newtons$

$180 \; Newtons$

Correct answer:

$180 \; Newtons$

Explanation:

This problem is solved using proportions.

$\frac{force}{mass}= \frac{45\; Newtons}{3\; kg}= \frac{x \; Newtons}{12\; kg}$

Cross multiply to get 540=3x and then divide by to get $x=180\; Newtons$

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High School Math : How to do word problems where one quantity is unknown

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

Example Question #11 : How To Do Word Problems Where One Quantity Is Unknown

Example Question #12 : How To Do Word Problems Where One Quantity Is Unknown

Example Question #11 : How To Do Word Problems Where One Quantity Is Unknown

Example Question #14 : Algebraic Equations

Example Question #12 : How To Do Word Problems Where One Quantity Is Unknown

Example Question #12 : How To Do Word Problems Where One Quantity Is Unknown

Example Question #14 : How To Do Word Problems Where One Quantity Is Unknown

Example Question #15 : How To Do Word Problems Where One Quantity Is Unknown

Example Question #16 : How To Do Word Problems Where One Quantity Is Unknown

Example Question #17 : How To Do Word Problems Where One Quantity Is Unknown

All High School Math Resources

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