A grandmother wants to spend at least $40 but no more than $60 on school clothes for her grandson. T-shirts sell for $10 and pants sell for $20. How many T-shirts and pants could she buy?

1 Answer
Sep 5, 2017

Using all of the $60

#color(white)(.)"2 pants and 2 T-shirts"#

#color(white)(.)"1 pants and 4 T-shirts"#

Explanation:

Let me introduce you to a couple of new terms. These tend to be used in the contexts of ranges of something.

In this case we have a maximum value: Term #->" Upper bound"#
In this case we have a minimum value: Term # ->" Lower bound"#

The difference between upper and lower bound is $20. This is the price of 1 pair of pants.

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#color(brown)("The maximum count of pants and uses upper bound")#

3 pants #->3xx$20=$60# which uses up all the money

2 pants #->2xx$20=$40# which is the least reduction of pants
#color(white)("ddddddddddddddddd")# and leaves $20 for T-shirts #->2 #T-shirts.

.......................................................................................
#color(brown)("The maximum count of T-shirts and uses upper bound")#

1 pants #->1xx$20=$20# which is the most reduction of pants
#color(white)("ddddddddddddddddd")#and leaves $40 for T-shirts #->4 #T-shirts

So we have

2 pants and 2 T_shirts
1 pants and 4 T_shirts