How do you solve it ?

Question

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:

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Answer 1 · 2017-12-05T21:00:20

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

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!