How do you solve it ?

Jack and two friends go to McDonald's, the options are:
OPTION 1 :2 HAMBURGERS AND 3 SODAS FOR 8 DOLLARS
OPTION 2: One more hamburger and one less soda with a dollar difference from Option 1.

If option 1 is more expensive, Jack and his friends determine that :
a hamburger costs USD:
And a soft drink costs USD:

1 Answer
Dec 5, 2017

The hamburger costs $1 and the soft drink costs $2.

Explanation:

We turn the two options to equations. We let h=hamburgers and s=soda(soft drink)

Option: 2 HAMBURGERS AND 3 SODAS FOR 8 DOLLARS

BECOMES

2h+3s=8

Option 2:One more hamburger and one less soda with a dollar difference from Option 1. And Option 1 is more expensive.

becomes

3h+2s=7

Since we have to eliminate one of the variables( we will go for h), we have to match the coefficient for the variable.

The LCM for 3 and 2 is 6.

2h+3s=8 becomes
3(2h+3s=8)=> 6h+9s=24

3h+2s=7 becomes
2(3h+2s=7)=>6h+4s=14

We now line up the equations and subtract them.
6h+9s=24
6h+4s=14
becomes
5s=10
s=$2

Plug this value in for one of the equations to get h=$1
This is the answer!