Question

Two numbers are in the ratio 5:2. One half of their sum is 10.5. Find the numbers.

Answer 1

well call the numbers x and y. you know 2x = 5y, right?

Answer 2

and what second equation can you write that describes their sum?

Answer 3

I am not sure about the second equation

Answer 4

what if I told you that the sum of the two numbers was 10.5, could you write that as an equation?

Answer 5

x+y=10.5

Answer 6

yes! so now, instead of "the sum of x and y", how can you write "half the sum of x and y"?

Answer 7

.5x+.5y=10.5

Answer 8

yep, that's it. now just solve that simultaneously with the first equation, 2x = 5y

Answer 9

I don't know how can u show me I haven't learned how to solve 2 variable equations

Answer 10

well if you multiply that whole equation through by 2 you get
5x + 5y = 21
then isolate x

5x = 21-5y
x = (21-5y)/5

Now you know x in terms of y, so substitute that expression (21-5y)/5 into the other equation 2x = 5y in place of x. You'll end up with a single equation with a single variable.

Answer 11

oh that make sense what do you do after

Answer 12

solve for x, then plug that value into either equation to find y

Answer 13

im confused

Answer 14

it does not give a whole number

Answer 15

thats ok

Answer 16

but the answer in the book is 15 & 6 but how

Answer 17

hi i'm back

Answer 18

so you know:

2x = 5y
0.5x + 0.5y = 10.5

multiply second equation by 2, you get
x + y = 21

isolate y, you get
y = 21-x

now substitute that into the second equation:
2x = 5y
2x = 5(21-x)
2x = 105 - 5x
7x = 105
x = 15

now use the original equation again:
x + y = 21
15 + y = 21
y = 6