Math CentralQuandaries & Queries


Question from Jada, a parent:

Hi, my daughter is having difficulties with a problem she is in the 5th grade, and insisted that it was a guess and check problem, but she really doesn't understand, and I don't either. Can you help us out?
Danielle is buying school supplies. She
has $7.25 to spend.
Notebook: $0.75
Pencils: $1.95
Pens: $2.50
Planner: $5.00
Please help by explaining the guess and check strategy for a problem like this. Thank you.

Hi Jada,

You didn't say so but I expect Danielle is to spend exactly all of the $\$7.25.$ Otherwise I would suggest buying a pen for $\$2.50$ and using the $\$4.75$ change to buy something nice for her mother. :)

My suggestion is that you start with the most expensive item, the planner which costs $\$5.00.$ This leaves $\$2.25$ left to spend. That's not enough to buy pens but she could buy pencils for $\$1.95$ leaving $\$0.30.$ She can't buy anything for 30 cents so that's not going to work. So after the planner she could but notebooks for $\$0.75$ each. How many could she but with $\$2.25?$

Suppose she doesn't but a notebook. She could buy two packages of pens for a total of $\$5.00$ Then you are back to $\$2,25$ change and you can spend it as you did in the previous paragraph.

She could buy only one package of pens for $\$2.50$ leaving $\$4.75$ left to spend. Can she buy pencils and notebooks to total $\$4.75?$

If she doesn't buy a planner or pens she can buy 1, 2 or 3 packages of pencils. In each case how much money does she have left? Is the remainder a multiple of $\$0.75?$

This is an exercise in keeping close and orderly track of the different possibilities. Starting with the most expensive item is a big help.

I hope my comments are useful. Write back if you need additional assistance.


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