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 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.

Penny

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