Question

MEDAL FOR HELP!!! Four numbers have a total of 92. The first number is twice the second number and the third number is 4 more than the sum of the first two. The fourth number is 3 less than the difference of the first two numbers. What are the numbers?

The first number is ___ , the second number is ___ ,
the third number is ____ , and the fourth number is ____ .

Answer 1

a = 26
b = 13
c = 43
d = 10

Answer 2

ok but how do you get that?

Answer 3

a+b+c+d = 92 "The four numbers have a total of 92"
2) a = 2b "The first number is twice the second number..."
3) c = (a+b)+4 "...the third number is 4 more than the sum of the first two."
4) d = (a-b)-3 "The fourth number is 3 less than the difference of the first two numbers."
Substitute equation 2) into equation 1) to get:
1a) 2b+b+c+d = 92 Simplify.
2a) 3b+c+d = 92 Now substitute equation 3 into this equation.
2b) 3b+(a+b)+4+d = 92 Simplify this.
2b) a+4b+d+4 = 92 Substitute equation 2) into this equation.
2c) 2b+4b+d+4 = 94 Simplify.
2c) 6b+d+4 = 92 Substitute equation 4) into this equation.

2d) 6b+((a-b)-3)+4 = 92 Substitute equation 2) into this equation.
2e) 6b+((2b-b)-3)+4 = 92 Simplify.
2e) 7b+1 = 92 Subtract 1 from both sides.
7b = 91 Divide both sides by 7.
b = 13
a = 2b = 2(13) = 26
c = (a+b)+4 = 26+13+4 = 43
d = (a-b)-3 = 26-13-3 = 10

Answer 4

do you understand?

Answer 5

hold on I'm trying....hmm

Answer 6

don't plagiarize tho if this is an essay lol

Answer 7

okay this is super confusing -_- sorry

Answer 8

lol no way this isn't an essay

Answer 9

read one step at a time

Answer 10

so this is what I'm getting
a= x
b= 2x
c= 2x + x + 4
d= 2x - x - 4

is this right? if so now how do i continue?

Answer 11

@valerievoun

Answer 12

let the 4 numbers are a,b,c,d

a+b+c+d = 92 --------(1)

a= 2b-------(2)

c= a+b+4 -----(3)
d= a-b-3 ----(4)

Answer 13

right, right ok now what

Answer 14

plug (2) in (3) and (4)

c= 3b+4------(5)

d= b-3------(6)

Answer 15

is it clear

Answer 16

do u understand

Answer 17

so what numbers are you adding?

Answer 18

i'm trying but this is so confusing :(

Answer 19

in (3)
c= a+b+4
c= 2b +b +4 [ from (2) a =2b ]
c= 3b +4 ----we are taking it as (5)
same way (6)

Answer 20

i explained above how we get (5)

Answer 21

if u understood that we go next step

Answer 22

@dayakar will guide you through it

Answer 23

respond quickly , do u get it or not

Answer 24

now plug (2) ,(5), and (6) in (1)

a+b+c+d= 92-----(1)
2b +b +3b+4 +b-3 = 92

7b+1 =92

7b= 91

b= 91/7

b= 13

Answer 25

You can put this solution on YOUR website!
Let the four numbers be a, b, c, and d.
From the problem description you can write:
1) a+b+c+d = 92 "The four numbers have a total of 92"
2) a = 2b "The first number is twice the second number..."
3) c = (a+b)+4 "...the third number is 4 more than the sum of the first two."
4) d = (a-b)-3 "The fourth number is 3 less than the difference of the first two numbers."
Substitute equation 2) into equation 1) to get:
1a) 2b+b+c+d = 92 Simplify.
2a) 3b+c+d = 92 Now substitute equation 3 into this equation.
2b) 3b+(a+b)+4+d = 92 Simplify this.
2b) a+4b+d+4 = 92 Substitute equation 2) into this equation.
2c) 2b+4b+d+4 = 94 Simplify.
2c) 6b+d+4 = 92 Substitute equation 4) into this equation.


2d) 6b+((a-b)-3)+4 = 92 Substitute equation 2) into this equation.
2e) 6b+((2b-b)-3)+4 = 92 Simplify.
2e) 7b+1 = 92 Subtract 1 from both sides.
7b = 91 Divide both sides by 7.
b = 13
a = 2b = 2(13) = 26
c = (a+b)+4 = 26+13+4 = 43
d = (a-b)-3 = 26-13-3 = 10
The numbers are:
a = 26
b = 13
c = 43
d = 10