Question

1.Three consecutive integers are such that when they they are taken in increasing order and multiplied by 2,3,4 respectively.and added become 74.find these numbers?

2.A person spent ₹564 in buying geese and ducks,if each cost ₹7 and each duck ₹3 and if the total number of birds bought was 108,how many of each type did he buy?

please solve this questions ​

Answer 1

Answer:

Let the three consecutive integers be x, x+1, x+2 in increasing order

Multiply 2,3,4 respectively

2(x)+3(x+1)+4(x+2)

This aad up to 74

2(x)+3(x+1)+4(x+2)=74

2x+3x+3+4x+8=74

9x+11=74

9x=74-11=63

X=63÷9=7

Therefore the three consecutive integers are 7,8,9

Answer 2

Answer:

1. let the first consecutive integer be=2x

let the second consecutive integer be=3x

let the third consecutive integer be=4x

They are added up to=74

2x+3x+4x=74

9x=74

${ \bold{let \: the \: first \: consecutive \: integer \: be = x + 1}} \\ { \bold{let \: the \: consecutive \: integer \: be = x + 2}} \\ { \bold{let \: the \: third \: consecutive \: integer \: be = x + 3 }}\\ { \bold{they \: are \: added \: up \: to = 74}} \\ { \bold{2(x + 1) + 3(x + 2) + 4(x + 3) = 74}} \\{ \bold{ 2x + 2 + 3x + 6 + 4x + 12 = 74}} \\ { \bold{9x + 20 = 74}} \\{ \bold{ 9x = 74 - 20}} \\ { \bold{9x = 54}} \\ {\bold{x = \frac{54}{9} }} \\ { \bold{x = 6}} \\ \\ { \bold{first \: consecutive \: integer = 2x +1= 2(6) + 1= 12 +1 \: = 13}} \\ { \bold{second \: consecutive \: integer = 3x+2 = 3(6) +2 = 18 + 2= 20}} \\ { \bold{third \: consecutive \: integer = 4x + 3 = 4(6) + 3= 24 +3 = 27}}$

Hope it will help you..