Math question

X + Y = 17 lbs

X = Y + 12 oz.

substitute and solve

This is an example of two equations with two unknowns. Solve for one in terms of the other and then substitute back into the first equation. I'll use S for small and L for large.

S=L-12
S+L=17, or -S=L-17

2L-29=0, L=29/2 or 14.5, substitute L back into the first formula
S=14.5-12 or 2.5

Check your work...
2.5 + 14.5 = 17 and 14.5-2.5 = 12
Check!

Alternatively, take away the extra weight first and divide the remaining weight by 2. That will give you the smaller weight.
(This is the method for "unequal sharing type 1" )

Method of solution (general)

Write down what you know
a) two packages
b) one is 12 oz more than other (difference)
c) both weigh 17 lbs (sum)

Write down what you want to know
weight of each package in pounds (lb) or ounces (lb).

Identify problems---have two kinds of units oz and lb--
good news--both are weights so convert one to pounds or other to oz
1 lb =16 oz
Difference is 12 oz * 1lb/16 ox=12/16 lb=(4*3)/(4*4) lb =4/4*3/4 lb = 3/4 lb

Identify packages as variables
easy enough Call them A & B , A is heavier package

Difference is 3/4 lb
so A-B=3/4=0.75
Sum is 17 lb
so A+B=17

Solve (By substitution)
2A=17.75lb & B=(17-17.75/2)lb

Check Answer

17.75/2+(17-17.75/2)=17 Sum OK
17.75/2-(17-17.75/2)=0.75 Difference OK

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