6th Grade Math Ratio Word Problems

Example:
Mark and Fred had some money in the ratio 6:1. Mark gave half of his money to Fred. Find the ratio of the amount of money Mark had left to the amount of money Fred had in the end.

Solution:

Before

After

 

The ratio of the amount of money Mark had left to the amount of money Fred had in the end is 3:4.

The following diagram gives another example of a ratio word problem solved using modeling.

 

How to solve ratio word problems?
Examples:

1. A board was cut into two pieces whose lengths are in the ratio 2:5. The longest piece was 85 inches. How long was the shortest piece?
   
   
2. At a track meet, 5/8 of the students were boys. There were 48 more boys. How many students were there altogether?
   
   
3. Theresa read two and one-fourth times as many pages on Saturday as on Sunday. She read 120 pages more on Saturday. How many pages did she read altogether?
   

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How to solve more difficult ratio word problems?
Examples:

1. The ratio of pigs to cows to sheep on the farm is 2:4:7. There are 65 more sheep than pigs. How many cows are there on the farm?
   
   
2. Archimedes, Hypatia and Zeno shared a sum of money. Archimedes received 1/6 of the money. Hypatia and Zeno shared the rest of the money in the ratio 2:3. Zeno got $7 more than Hypatia. How much money did they share altogether?
   
   
3. One-third of Elmer’s age is the same as two-fifths of Sam’s age.
   a) Draw a bar model representing the situation
   b) Elmer is 5 years older than Sam. How old is Sam?
   

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How to use proportions to solve ratio problems?

1. At Al’s Catering Service, they often make a large batch of fruit salad. The ratio of cups of apples to cups of oranges in the recipe is 8 : 5.
   a) If they use 15 cups of oranges, how many cups of apples should they use?
   b) If they only use 2 cups of apples, how many cups of oranges should they use?
   

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Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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