Question

A box of candies contains only chocolates, licorice sticks, peppermints, and gummy bears. If 1/4 of the candies are chocolates, 1/6 of the candies are gummy bears, 1/3 are peppermints, and 9 are licorice sticks, what is the product of the number of peppermints and the number of chocolates?

Answer 1

Givens

Let the total number of Candies = T

1/4 T = chocolates

1/6 T = gummy bears

1/3T = peppermints

9 = Licorice Sticks.

Equation

1/4 T + 1/6T + 1/3 T + 9 = T

Solve

The Lowest common denominator on the left side is

4 = 2*2

6 = 2*3

3 = 3

LCM = one 3 two 2s

LCM = 3*2*2

LCM = 12

Change the fractions to 12ths.

$\dfrac{1*3}{4*3} =\dfrac{3}{12}$

$\dfrac{1*2}{6*2} =\dfrac{2}{12}$

$\dfrac{1*4}{4*3} =\dfrac{4}{12}$

3/12 T + 2/12 T + 4/12 T + 9 = T

(3 + 2 + 4)*T/12 + 9 = T

9/12 T + 9 = T Subtract 9/12 T from both sides.

9 = T - 9/12 T

9 = 3/12 T

9 = 1/4 T Multiply both sides by 4

T = 36

1/3 T = Peppermints

1/3 * 36 = Peppermints.

12 = Peppermints.

1/4 T = chocolates

1/4 36 = chocolates

9 = chocolates.

Answer

Product 12 * 9 = 108 <<<<<<< Answer

The product of chocolates and Peppermints = 108