Question

Write as an equation:

1. the sum of 2 numbers is 164. the larger exceeds 3 times the smaller by 36.

2. the sum of 2 numbers is 120. 4 times the larger divided by twice the smaller number is 34.

Answer 1

1.
`x= 3(164-x)+36`

2.
`(4(120-b))/(2b)=34`

Explanation:

The sum means two number are adding up.

Exceeds means subtraction.

1.Let the number larger number of x and other number y

x + y =164.. (1)

x - 3y = 36...(2)

x= 3y + 36

Putting value of x from (2) into (1).

So ,according to question we got equation:

x=3(164-x)+36

2. Let the number larger number of a and other number b

a + b = 120 ..(1)

`(4a)/(2b)=34`..(2)

Putting value of a from (1) into (2)

So ,according to question we got equation:

`(4(120-b))/(2b)=34`

Answer 2

Answer: 1) 132 and 32

`\bold{2) (340)/(3) and (20)/(3)}`

Explanation:

Let x represent the larger number and y represent the smaller number.

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1)

x + y = 164 and x = 3y + 36

(3y + 36) + y = 164

36 + 4y = 164

4y = 128

y = 32 and x = 3(32) + 36

x = 96 + 36

x = 132

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2)

x + y = 120 and
`(4x)/(2y)=34` ⇒ 4x = 68y ⇒ x = 17y

(17y) + y = 120

18y = 120

`y=(120)/(18)`

`y=(20)/(3)` and
`x=17 \bigg( (20)/(3) \bigg)`

`x= (340)/(3)`