Question

janice buys 74 packs of gum in a variety of flavors. she chooses twice as many packs of green apple gum as packs of spearmint gum and 6 fewer packs of cinnamon gum that packs of green apple gum. How many packs of spearmint gum does janice buy?

Answer 1

A) 16

Explanation:

g= green apple

c= cinnamon

s= spearmint

74=g+c+s

g=2s

g-6=c

so we can replace c in the equation

74=g+g-6+s (because c=g-6)

we can also replace g in the equation

2s+2s-6+s=74 (because g=2s)

so, 5s-6=74 (add 6 to both sides)

5s=80 (divide by 5)

s=16

Answer 2

Answer: Hello there!

Let's define G has the number of packs of green apple, S as the number of packs of spearmint, and C as the number of packs of cinnamon.

Now we want to know the number of spearmint gum packs that Janice buys:

We know that:

G + S + C = 74

G = 2S

G - C = 6

Now we have a system of 3 equations and 3 variables, let's solve it.

In the second equation we can remove G of the equations, and replace it in the first and third equation:

G + S + C = 74

2S + S + C = 74

3S + C = 74

and

G - C = 6

2S - C = 6

Now we only have two equations, lets isolate C in the second equation

2S - C = 6

C = 2S - 6

now we can replace it in the first equation, and solve it for S

3S + C = 74

3S + 2S - 6 = 74

5S = 74 + 6 = 80

S = 80/5 = 16

She buy's 16 packs of spearmint gum.