# USING RATIO REASONING TO SOLVE PROBLEMS

## About "Using ratio reasoning to solve problems"

Using ratio reasoning to solve problems :

Ratio reasoning is nothing but a proportion which states that two ratios or rates are equivalent.

Examples :

1/3 and 2/6 are equivalent ratios

1/3  =  2/6 is a proportion

Here, we are going to see how ratio reasoning (proportion) can be used to solve problems.

## Using ratio reasoning to solve problems - Examples

Example 1 :

Sheldon and Leonard are partners in a business. Sheldon makes \$2 in profits for every \$5 that Leonard makes. If together they make a profit of \$28 on the first item they sell, how much profit does Sheldon make ?

Solution :

Step 1 :

Given : Sheldon’s profit is \$2 and Leonard's profit is \$5

Total profit  =  2 + 5  =  \$7

The ratio of Sheldon’s profit to the total profit is

\$2 / \$7

Let "S" be the Sheldon's profit for the given total profit \$28.

Then, we have

Step 2 :

Let us use ratio reasoning to find "S".

Because \$7 × 4 = \$28, multiply \$2 by 4.

Therefore, if they make a total profit of \$28, then Sheldon makes a profit of \$8.

Example 2 :

The members of the PTA are ordering pizza for a meeting. They plan to order 2 cheese pizzas for every 3 pepperoni pizzas they order. How many cheese pizzas will they order if they order a total of 25 pizzas ?

Solution :

Step 1 :

Given : 2 cheese pizzas for every 3 pepperoni pizzas

Total profit  =  2 + 3  =  5 pizzas

The ratio of cheese pizzas to total pizzas is

2 / 5

Let "C" be the number of cheese pizzas for the given total pizzas 25.

Then, we have

Step 2 :

Let us use ratio reasoning to find "C".

Because 5 × 5 = 25, multiply 2 by 5.

Therefore, if they order a total of 25 pizzas, then they will order 10 cheese pizzas.

After having gone through the stuff given above, we hope that the students would have understood "How to use ratio reasoning to solve problems".

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WORD PROBLEMS

HCF and LCM  word problems

Word problems on simple equations

Word problems on linear equations

Algebra word problems

Word problems on trains

Area and perimeter word problems

Word problems on direct variation and inverse variation

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Word problems on comparing rates

Converting customary units word problems

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Ratio and proportion word problems

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Percent of a number word problems

Word problems on constant speed

Word problems on average speed

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Percentage shortcuts

Times table shortcuts

Time, speed and distance shortcuts

Ratio and proportion shortcuts

Domain and range of rational functions

Domain and range of rational functions with holes

Graphing rational functions

Graphing rational functions with holes

Converting repeating decimals in to fractions

Decimal representation of rational numbers

Finding square root using long division

L.C.M method to solve time and work problems

Translating the word problems in to algebraic expressions

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Remainder when 17 power 23 is divided by 16

Sum of all three digit numbers divisible by 6

Sum of all three digit numbers divisible by 7

Sum of all three digit numbers divisible by 8

Sum of all three digit numbers formed using 1, 3, 4

Sum of all three four digit numbers formed with non zero digits

Sum of all three four digit numbers formed using 0, 1, 2, 3

Sum of all three four digit numbers formed using 1, 2, 5, 6