RATIO PROBLEMS

MONEY

Concept: A ratio is a comparison of two numbers. It can be written in several ways. For example, when comparing the numbers 1 and 2, we can express the comparison as 1 to 2, or 1 : 2 or ½.

Always write the terms of the ratio in the same order as the problem compares them.

Just as we can reduce fractions to lowest terms, we can simplify ratios to their lowest terms, although a ratio with a denominator of 1 must still be expressed as a fraction, and ratios that appear to be improper fractions must be left as improper fractions.

Many ratio problems require more than one step.

You may not be given both of the numbers that you need to write a ratio. In this case, you may need to solve another equation to find the missing number.

Finally, when two ratios are written as equal ratios, the equation is called a proportion. For example, is a proportion. In many proportion problems, one of the four terms is missing.

The proportion can be solved using the Cross-product Rule.

Cross-product Rule
To find the missing number in a proportion, cross multiply, and divide the product by the third number. For example, in the proportion , first multiply . Then divide . In this problem .

Steps for Solving Simple Ratio Problems

Step 1 | Set up the ratio, writing the terms in the same order that the problem compares the terms.
Step 2 | Simplify the ratio to its lowest terms. (Remember that a ratio with a denominator of 1 must still be expressed as a fraction, and ratios that appear to be improper fractions must be left as improper fractions.)

Steps for Solving Multiple Step Ratio Problems

Step 1 | Set up the first ratio, writing the terms in the same order that the problem compares the terms.
Step 2 | Set up an equation to solve for the unknown number needed for the ratio.
Step 3 | Set up a ratio, writing the terms in the same order that the problem compares the terms.
Step 4 | Simplify the ratio to its lowest terms. (Remember that a ratio with a denominator of 1 must still be expressed as a fraction, and ratios that appear to be improper fractions must be left as improper fractions.)

Steps for Solving Simple Proportion Problems

Step 1 | Form a proportion using two ratios. Use X for the unknown number.
Step 2 | Apply the Cross-product Rule to solve for X.

Steps for Solving Multistep Proportion Problems

Step 1 | Set up the first ratio using given information.
Step 2 | Set up an equation, if necessary, to solve for any unknown information.
Step 3 | Set up another ratio, if necessary, using the new information.
Step 4 | Form a proportion using two ratios. Use the ratio from either Step 1 or Step 3 for the first ratio in the proportion, and another ratio, set up in the same order, while substituting X for the unknown number.
Step 5 | Apply the Cross-product Rule to solve for X.

Example1: When Francesca landed in Taiwan she exchanged 130 euros for 37950 Yuan. What was the rate of exchange in Yuan per Euros? Use whole numbers only.

Use the Steps for Solving Simple Ratio Problems

Step 1 | Set up the ratio, writing the terms in the same order that the problem compares the terms.
We know that 130 Euros yielded 37950 Yuan.
Step 2 | Simplify the ratio to its lowest terms. (Remember that a ratio with a denominator of 1 must still be expressed as a fraction, and ratios that appear to be improper fractions must be left as improper fractions.)
To find the missing number in a proportion, cross multiply,
and divide the product by the third number.
In the proportion, X is equal to 292.
The rate of exchange in Yuan per Euros is 292 Yuans per 1 Euro. In the Math Scaffolding Program, enter 292 into the first box, and 1 into the second.

Example 2: Taquitos cost 45.47 Yen each. The exchange rate is 2 Yens per 1 Swiss Franc. How much did the taquitos cost in Swiss Francs? Round the answer to the hundredth of a Swiss Franc.

Use the Steps for Solving Simple Proportion Problems

Step 1 | Form a proportion using two ratios. Use X for the unknown number.
We will designate the top number in each ratio as Swiss Franc, and the bottom number in each ratio as Yen.
We will set up a proportion, keeping using the same designations as above.
Step 2 | Apply the Cross-product Rule to solve for X.
To find the missing number in a proportion, cross multiply,
and divide the product by the third number.
In the proportion, X is equal to 22.735. Round the answer to the hundredth of a Swins Francs. 22.735 rounded to the hundredth is 22.74
At an exchange rate of 2 Yen to 1 Swiss Francs, a taquito which costs 45.47 Yens will cost 22.74.

Example 3: The 13 lb bottle cost 57 centavos. For 25 centavos an 11 lb bottle can be purchased. Which size bottle is the better buy? Answer with the amount of the weight of the bottle.

Use the Steps for Solving Simple Proportion Problems

We will use the Steps for Solving Simple Proportion Problems twice in this problem. We will determine how many centavos it will cost for one lb. We will then compare results to determine which lb is cheaper. That one will be the better buy.
Step 1 | Form a proportion using two ratios. Use X for the unknown number.
We will designate the top number in each ratio as lb, and the bottom number in each ratio as centavos.
We will set up a proportion, keeping using the same designations as above.
Step 2 | Apply the Cross-product Rule to solve for X.
To find the missing number in a proportion, cross multiply,
and divide the product by the third number.
In the proportion, X is equal to 4.38.
Now repeat this process with the 11lb bottle which costs 25 centavos.
Step 1 | Form a proportion using two ratios. Use X for the unknown number.
We will designate the top number in each ratio as lb, and the bottom number in each ratio as centavos.
We will set up a proportion, keeping using the same designations as above.
Step 2 | Apply the Cross-product Rule to solve for X.
To find the missing number in a proportion, cross multiply,
and divide the product by the third number.
In the proportion, X is equal to 2.27.
One lb of the 13 lb bottle costs 4.38 Centavos. One lb of the 11 lb bottle costs only 2.27 Centavos. Therefore, the 11 lb bottle is the better buy.