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Answer :
Sure, let's solve these problems step-by-step:
1. If 8 cases of merchandise cost [tex]$60, what would a dozen (12) cases cost?
- First, we find the cost per case:
\[
\text{Cost per case} = \frac{60}{8} = 7.5 \, \text{dollars per case}
\]
- Next, find the cost for 12 cases:
\[
\text{Total cost for 12 cases} = 12 \times 7.5 = 90 \, \text{dollars}
\]
2. Benito saves $[/tex]6 out of every [tex]$20 he earns. He earned $[/tex]90 one month. How much did he save?
- First, find the savings rate:
[tex]\[
\text{Savings rate} = \frac{6}{20} = 0.3
\][/tex]
- Next, find out how much he saved from [tex]$90:
\[
\text{Savings} = 0.3 \times 90 = 27 \, \text{dollars}
\]
3. A man who is 6 feet tall casts a shadow that is 11 feet long. At the same time, a tree casts a shadow that is 33 feet long. What is the height of the tree?
- Set up the proportion:
\[
\frac{\text{Height of the man}}{\text{Shadow of the man}} = \frac{\text{Height of the tree}}{\text{Shadow of the tree}}
\]
- Use the given values to solve for the height of the tree:
\[
\frac{6}{11} = \frac{\text{Height of the tree}}{33}
\]
- Cross-multiply and solve for the height of the tree:
\[
\text{Height of the tree} = 6 \times \frac{33}{11} = 18 \, \text{feet}
\]
4. Mr. Savage used 3 gallons of paint to cover 1,350 square feet of wall space. At this rate, how much paint will be needed to cover 1,800 square feet?
- First, find the rate of paint usage:
\[
\text{Rate of paint usage} = \frac{3 \text{ gallons}}{1350 \text{ square feet}}
\]
- Next, use this rate to find the amount of paint needed for 1,800 square feet:
\[
\text{Paint needed} = 3 \times \frac{1800}{1350} = 4 \,\text{gallons}
\]
5. In his last game, the Rams' quarterback completed 10 out of 18 passes he threw. At this rate how many passes will he attempt if he completes 15 passes?
- Find the completion rate:
\[
\text{Completion rate} = \frac{10}{18}
\]
- Use this rate to find the number of passes he will attempt to complete 15 passes:
\[
\text{Passes attempted} = \frac{15}{\frac{10}{18}} = 27 \, \text{passes}
\]
6. Serena paid a tax of $[/tex]288 on a house assessed at [tex]$48,000. Using the same tax rate, find the tax on a house assessed at $[/tex]59,000.
- First, find the tax rate:
[tex]\[
\text{Tax rate} = \frac{288}{48000}
\][/tex]
- Use this tax rate to find the tax for a house assessed at [tex]$59,000:
\[
\text{Tax} = \frac{288}{48000} \times 59000 = 354 \,\text{dollars}
\]
So the final answers are:
1. $[/tex]90.00
2. [tex]$27.00
3. 18 feet
4. 4 gallons
5. 27 passes
6. $[/tex]354.00
1. If 8 cases of merchandise cost [tex]$60, what would a dozen (12) cases cost?
- First, we find the cost per case:
\[
\text{Cost per case} = \frac{60}{8} = 7.5 \, \text{dollars per case}
\]
- Next, find the cost for 12 cases:
\[
\text{Total cost for 12 cases} = 12 \times 7.5 = 90 \, \text{dollars}
\]
2. Benito saves $[/tex]6 out of every [tex]$20 he earns. He earned $[/tex]90 one month. How much did he save?
- First, find the savings rate:
[tex]\[
\text{Savings rate} = \frac{6}{20} = 0.3
\][/tex]
- Next, find out how much he saved from [tex]$90:
\[
\text{Savings} = 0.3 \times 90 = 27 \, \text{dollars}
\]
3. A man who is 6 feet tall casts a shadow that is 11 feet long. At the same time, a tree casts a shadow that is 33 feet long. What is the height of the tree?
- Set up the proportion:
\[
\frac{\text{Height of the man}}{\text{Shadow of the man}} = \frac{\text{Height of the tree}}{\text{Shadow of the tree}}
\]
- Use the given values to solve for the height of the tree:
\[
\frac{6}{11} = \frac{\text{Height of the tree}}{33}
\]
- Cross-multiply and solve for the height of the tree:
\[
\text{Height of the tree} = 6 \times \frac{33}{11} = 18 \, \text{feet}
\]
4. Mr. Savage used 3 gallons of paint to cover 1,350 square feet of wall space. At this rate, how much paint will be needed to cover 1,800 square feet?
- First, find the rate of paint usage:
\[
\text{Rate of paint usage} = \frac{3 \text{ gallons}}{1350 \text{ square feet}}
\]
- Next, use this rate to find the amount of paint needed for 1,800 square feet:
\[
\text{Paint needed} = 3 \times \frac{1800}{1350} = 4 \,\text{gallons}
\]
5. In his last game, the Rams' quarterback completed 10 out of 18 passes he threw. At this rate how many passes will he attempt if he completes 15 passes?
- Find the completion rate:
\[
\text{Completion rate} = \frac{10}{18}
\]
- Use this rate to find the number of passes he will attempt to complete 15 passes:
\[
\text{Passes attempted} = \frac{15}{\frac{10}{18}} = 27 \, \text{passes}
\]
6. Serena paid a tax of $[/tex]288 on a house assessed at [tex]$48,000. Using the same tax rate, find the tax on a house assessed at $[/tex]59,000.
- First, find the tax rate:
[tex]\[
\text{Tax rate} = \frac{288}{48000}
\][/tex]
- Use this tax rate to find the tax for a house assessed at [tex]$59,000:
\[
\text{Tax} = \frac{288}{48000} \times 59000 = 354 \,\text{dollars}
\]
So the final answers are:
1. $[/tex]90.00
2. [tex]$27.00
3. 18 feet
4. 4 gallons
5. 27 passes
6. $[/tex]354.00
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