 # Problem of the Week Problem A and Solution Creating an Art Kit

## Problem

A teacher at Sioux Mountain School wants to purchase items for art kits to be used in their classroom. Below is a list of the items in one kit, along with the price for each item. All prices include tax.

 Pencil crayons $$\1.75$$ Sketch book $$\2.25$$ Watercolour paints $$\3.15$$ Glue $$\1.10$$ Scissors $$\1.70$$

If the teacher has a budget of $$\80$$ for art supplies, then estimate how many kits they can make. Justify your answer. ## Solution

One way to estimate how much each kit will cost is to round the price of each item to the nearest dollar:

 Pencil crayons $$\2$$ Sketch book $$\2$$ Watercolour paints $$\3$$ Glue $$\1$$ Scissors $$\2$$

Thus, each art kit will cost approximately $$\2 + \2 + \3 + \1 + \2 = \10$$.

With a budget of $$\80$$ and since $$80 \div 10 = 8$$, we estimate they can make $$8$$ art kits.

Teacher’s Notes

When we use estimation we need to realize that our estimated result is an approximation and not an absolute guarantee of a correct answer. We should always consider a margin of error for our estimations.

For example, in this problem if you calculate the actual cost of an art kit, it comes to: $1.75 + 2.25 + 3.15 + 1.10 + 1.70 = \9.95$

In this case, our estimation gave us the actual number of art kits that the teacher can purchase. However, if the cost of the paints was actually $$\3.25$$, instead of $$\3.15$$, then the actual cost of an art kit would be $$\10.05$$, but our estimate would still be $$\10$$. This is a reasonable estimation, but the actual cost means the teacher does not have the budget for $$8$$ kits, but rather for only $$7$$ kits.

Since we used estimation to predict the number of kits that could be purchased, it would be more accurate to give an answer of $$8$$ kits, plus or minus $$1$$ kit. This factors in the margin of error.