**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.

**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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