Solve the problem. See Examples.EXAMPLE Finding the Number of Orders for TeaThe owner of T...

Solve the problem. See Examples.

EXAMPLE Finding the Number of Orders for Tea

The owner of Terry’s Coffeehouse found that on one day the number of orders for tea was the number of orders for coffee. If the total number of orders for the two drinks was 76, how many orders were placed for tea?

Step 1 Read the problem. It asks for the number of orders for tea.

Step 2 Assign a variable. Because of the way the problem is stated, let the variable represent the number of orders for coffee.

Step 3 Write an equation. Use the fact that the total number of orders was 76.

Step 4 Solve.

Step 5 State the answer. In this problem, x does not represent the quantity that we are asked to find. The number of orders for tea was . So (57) = 19 is the number of orders for tea.

Step 6 Check. The number of orders for tea, 19, is one-third the number of orders for coffee, 57, and 19 + 57 = 76. Since this agrees with the information given in the problem, the answer is correct.

EXAMPLE Analyzing a Gasoline-Oil Mixture

A lawn trimmer uses a mixture of gasoline and oil. The mixture contains 16 oz of gasoline for each 1 ounce of oil. If the tank holds 68 oz of the mixture, how many ounces of oil and how many ounces of gasoline does it require when it is full?

Step 1 Read the problem. We must find how many ounces of oil and gasoline are needed to fill the tank.

Step 2 Assign a variable.

A diagram like the following is sometimes helpful.

Step 3 Write an equation.

Step 4 Solve.

Step 5 State the answer. The lawn trimmer requires 4 oz of oil, and 16(4) = 64 oz of gasoline when full.

Step 6 Check. Since 4 + 64 = 68, and 64 is 16 times 4, the answer checks.

U.S. five-cent coins are made from a combination of two metals: nickel and copper. For every 1 pound of nickel, 3 lb of copper are used. How many pounds of copper would be needed to make 560 lb of five-cent coins? (Source: The United States Mint.)