# The sum of three integers is 220. The sum of the first and second integers exceeds the third by...

## Question:

The sum of three integers is {eq}220 {/eq}. The sum of the first and second integers exceeds the third by {eq}94 {/eq}. The third integer is {eq}55 {/eq} less than the first.

Find the three integers.

## Algebraic equation word problems

An algebraic equation is formed when a relation between any variable is equated to a constant.

In the word problems of algebraic equation, this relation is given in statement and we need to form an algebraic equation out of it. Assuming a base variable and determining other unknowns in its term also helps in simplifying the equation.

For example: 4x +3y = 1 is an algebraic equation where x and y are variables and 1 is the equivalent constant of the relation shown in the equation.

Let the three numbers be {eq}a,\ b,\ {/eq} and {eq}c. {/eq}

According to the problem statement sum all three numbers is {eq}220: {/eq}

$$a + b+ c = 220$$

According to the problem statement sum of the first and second integers exceeds the the third by {eq}94:{/eq}

$$a + b = c + 94$$

Using the value of {eq}a+b {/eq} in the equation {eq}a + b+ c = 220. {/eq}

$$a + b+ c = 220$$

$$94 + c + c = 220$$

$$2c = 220 - 94$$

$$2c = 126$$

$$c = 63$$

According to the problem statement, The third integer is {eq}55 {/eq} less than the first.

$$a - c =55$$

Using the value {eq}c=63 {/eq}

$$a - c =55$$

$$a - 63 =55$$

$$a =55 +63$$

$$a =118$$

Using the values of {eq}a {/eq} and {eq}c {/eq} in the equation {eq}a + b+ c = 220 {/eq}

$$a + b+ c = 220$$

$$118 + b+ 63 = 220$$

$$b = 220 - 118 - 63$$

$$b = 39$$

The three numbers are {eq}118,\ 39,\ {/eq} and {eq}63. {/eq} 