Tania bought 4 more pounds of pears than Wilma. Together, Tania and Wilma bought 18 pounds of pears. How many pounds of pears did Wilma buy?

2 Answers
Mar 1, 2018

Wilma bought 7 pounds of pears.

Explanation:

Let pounds bought by Wilma be #x#.
Then those bought by Tania will be #x+4#

So we have:

#x+x+4=18#
#2x+4=18#
#2x=14#
#x=7#

So Wilma bought 7 pounds of pears.

Mar 1, 2018

Tanya has #11# pounds of pears
Wilma has #7# pounds of pears

Explanation:

Let Tania's pounds of pears be #t#

Let Wilma's pounds of pears #w#

The first sentence, "Tania bought 4 more pounds of pears than Wilma" can be written as:

#t=w+4#

The second sentence, "Tania bought 4 more pounds of pears than Wilma" can be written as:

#t+w=18#

So, the two equations we have are:

#t=w+4#
#t+w=18#

Multiply the second equation by #-1#

#t=w+4#

#-t-w=-18#

Now, we add both the simultaneous equations:

#(t)+(-t)+(-w)=(4)+(-18)+(w)#

#t-t-w=4-18+w#

#t# and #-t# cancel out:

#-w=-14+w#

#-2w=-14#

#2w=14#

#w=7#

Now that we have one variable, we can substitute it inside any one of the equations. Let us take the first equation, as #t# is alone, and it would be easier to manipulate it:

#t=w+4#

Since #w=7#:

#t=7+4#

#t=11#

Thus, Tanya has #11# pounds of pears.
Thus, Wilma has #7# pounds of pears