Lower Elementary:
Question: If you buy 4 marbles for 75 cents each, how much change will you get back from a $5 bill?
Answer: $2
Solution: First find out how much the 4 marbles cost altogether. Count by 75, 4 times to get the total amount of the four marbles. 75, 150, 225, 300. Alternatively, counting something 4 times is the same as doubling twice. 75 doubled is 150, and 150 doubled is 300. The 4 marbles cost 300 cents, or $3. If you spend $5, you will get $2 back in change ($5 – $3 = $2).
Upper Elementary:
Question: A farmer harvested 2,160 apples. The apples are sold for $10 a dozen. How much money will the farmer make if all the apples are sold?
Answer: $1,800
Solution: First, we need to see how many groups of 12 the farmer can make (since there are 12 in a dozen). Divide the total amount of apples by 12. 2,160 ÷ 12 = 180, so the farmer has 180 groups of 12 apples. Multiply 180 by $10 to get how much money the farmer will make. 180 × $10 = $1,800.
Middle School:
Question: Four fifths of a number when reduced by 12 is 36. What is the number?
Answer: 60
Solution:
Algebraic solution:
If we write the sentence as an equation and let x be the number, we get
4/5x – 12 = 36
Add 12 to both sides
4/5x = 48
Multiply both sides by 5/4 (the reciprocal of 4/5 so that x is by itself)
x = 48 × 5/4 = 60
The mystery number is 60.
Number sense solution:
4/5 of a number is the same as dividing the number by 5 and multiplying by 4. Another way of reading the problem is a number divided by 5, times 4, minus 12 is 36. We will work our way backwards to figure out the mystery number:
What minus 12 is 36? 48 minus 12 is 36, so the number divided by 5, times 4 is 48.
What times 4 is 48? 12 times 4 is 48, so the number divided by 5 is 12.
What divided by 5 is 12? 60 divided by 5 is 12, so our mystery number is 60.
Algebra and Up:
Question: How many sides does a regular polygon have if the measure of each angle is 170°?
Answer: 36 sides
Solution: The total number of degrees in a polygon is given by 180(n-2) where n is the number of sides. A regular polygon has all angles the same. To find the measure of each angle, divide the total degrees by the number of sides: (180(n-2))/n = measure of one angle. Since we know how much one angle is, solve for n to get the number of sides the polygon has.
(180(n-2))/n = 170
180(n-2) = 170n
180n – 360 = 170n
10n – 360 = 0
10n = 360
n = 36
The polygon has 36 sides.
