Basic Arithmetic : Ratios and Rates

Study concepts, example questions & explanations for Basic Arithmetic

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Example Questions

Example Question #1 : Ratio Tables

Find the value of  in the following ratio table:

 

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Possible Answers:

Correct answer:

Explanation:

The numbers on the left side to the numbers on the right side are in a ratio of 1 to 7. In other words, multiply the numbers on the left by 7 to get the numbers on the right.

Using that ratio, we arrive at the following equation for x:

 

Now, divide both sides by 7.

Example Question #52 : Basic Arithmetic

Find the value of  in the ratio table above.

Possible Answers:

Correct answer:

Explanation:

To find , we can set up the following ratios:

Now, cross-multiply and solve.

Example Question #11 : Ratios And Rates

              

 

Find the value of  in the ratio table above.

Possible Answers:

Correct answer:

Explanation:

To find the multiplier, divide two numbers from the same row:

Now, multiply this by  and set that equal to 

Divide both sides by 

Example Question #2 : Ratio Tables

                   

In the ratio table above, find .

Possible Answers:

Correct answer:

Explanation:

To figure out the ratio, divide the second column by the first.

Since we are multiplying the first column by  to get the second column, we can set up the following equation for .

Multiply both sides by 7.

Example Question #4 : Ratio Tables

                         
                       

Find the value of  in the ratio table above.

Possible Answers:

Correct answer:

Explanation:

To find , we can set up the following ratio:

Now, cross multiply and solve.

Example Question #11 : Ratios And Rates

I put  in a bank account at a  annual simple interest rate. How much interest will have accumulated after two years?

Possible Answers:

Correct answer:

Explanation:

This is a simple interest rate problem, for which we use the formula:

Interest = P x r x t

P is the principal, or original loan amount; r is the annual interest rate; and t is the number of years in question.

In this problem, P = $9,000; r = 4%; and t = 2 years. Plugging these into the formula gives us:

So, after two years the account has gathered $720 in interest.

Example Question #61 : Basic Arithmetic

If  painters can paint  houses in  day, how many painters would it take to paint  houses in  day?

Possible Answers:

Correct answer:

Explanation:

We can set up the following proportions using the given information:

Now, cross multiply these two fractions to get the following equation:

Divide both sides by .

Example Question #2 : Linear Equations With Ratios And Rates

If a car travels at  miles per hour, how many hours would it take the car to travel  miles?

Possible Answers:

Correct answer:

Explanation:

We can write 40 miles per hour as the following fraction:

Since we want to figure out how many hours it takes a car to travel 200 miles, we can write the following equation:

Now, cross multiply.

Divide both sides by 40.

Example Question #2 : Linear Equations With Ratios And Rates

If one recipe calls for  eggs to make  waffles, how many eggs are needed to make  waffles?

Possible Answers:

Correct answer:

Explanation:

To solve this problem, we can set up a proportion.

That proportion will tell us how many eggs go into each waffle. Since the number of eggs that goes into each waffle doesn't change, we can set these two proportions equal to each other.

Now, fill it in with the information we know:

For the sake of making math easier, drop the words so we get the following equation:

To solve for x, cross-multiply this equation.

Divide both sides by 18.

Example Question #1 : Linear Equations With Ratios And Rates

The ratio of boys to girls in a class is . If there are  boys in the class, how many girls are in the class?

Possible Answers:

Correct answer:

Explanation:

We can write the following equation using the ratios given:

 is the number of girls in the class.

Now, we can cross multiply to get the following equation:

Now divide both sides by .

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