Certainly! Let's go through each problem and solve them one by one.

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1. The ratio of boys to girls is 3 to 2. If there are 12 boys, how many girls are there?

The ratio of boys to girls is given as $3:2$.

Let $x$ represent the number of girls. Set up a proportion: $\frac{3}{2} = \frac{12}{x}$

Cross-multiply to solve for $x$: $3x = 2 \times 12$ $3x = 24$ $x = 8$

Answer: There are 8 girls.

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2. It takes one Super Giant Pizza to feed 3 people. If you invite 36 people, how many pizzas will you need?

Let $x$ represent the number of pizzas needed. Set up a proportion: $\frac{1}{3} = \frac{x}{36}$

Cross-multiply to solve for $x$: $3x = 36$ $x = 12$

Answer: You will need 12 pizzas.

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3. At a recent party, it cost $9.50 for refreshments for 10 guests. At this rate, how much would it cost to have refreshments for 80 guests?

Let $x$ represent the cost for 80 guests. Set up a proportion: $\frac{9.50}{10} = \frac{x}{80}$

Cross-multiply to solve for $x$: $10x = 9.50 \times 80$ $10x = 760$ $x = 76$

Answer: It would cost $76 for refreshments for 80 guests.

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4. Mary has saved $17.50 in the past 3 weeks. At this rate, how much will she save in 15 weeks?

Let $x$ represent the amount she will save in 15 weeks. Set up a proportion: $\frac{17.50}{3} = \frac{x}{15}$

Cross-multiply to solve for $x$: $3x = 17.50 \times 15$ $3x = 262.5$ $x = 87.5$

Answer: She will save $87.50 in 15 weeks.

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5. Mr. Johnson was paid $190 for a job that required 40 hours of work. At this rate, how much should he be paid for a job requiring 60 hours of work?

Let $x$ represent the amount he should be paid for 60 hours of work. Set up a proportion: $\frac{190}{40} = \frac{x}{60}$

Cross-multiply to solve for $x$: $40x = 190 \times 60$ $40x = 11400$ $x = 285$

Answer: He should be paid $285 for 60 hours of work.

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Would you like a detailed explanation of any specific problem, or do you have any questions about the solutions?

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Here are 5 related questions to expand on these concepts:

1. If the ratio of students to teachers in a school is 20:1, how many teachers are there if there are 600 students?
2. If 8 pizzas can feed 24 people, how many pizzas are needed to feed 96 people?
3. If a person spends $45 to feed 15 guests, what would it cost to feed 45 guests?
4. If Tom saves $25 in 5 weeks, how much would he save in 20 weeks?
5. If a worker is paid $300 for 50 hours, how much would they be paid for 75 hours?

Tip: When working with ratios and proportions, always set up your ratios carefully and cross-multiply to find the missing value. This method works well for most proportion problems.