Question

A welcome kit contains 3 grocery store and seven drugstore coupons. The coupons are worth $45. Another welcome kit contains three grocery store coupons and six drugstore coupons worth $42. What is the value of each grocery coupon and each drug store coupon?

Answer 1

Answer:

The value of each grocery store coupon is $6

Then the value of each drugstore coupon is $3.

Step-by-step explanation:

Let's define:

G = value of a grocery store coupon.

D = value of a drugstore coupon.

We know that:

"A welcome kit contains 3 grocery store and seven drugstore coupons. The coupons are worth $45"

We can write this as:

3*G + 7*D = $45

And we also know that:

"Another welcome kit contains three grocery store coupons and six drugstore coupons worth $42"

We can write this as:

3*G + 6*D = $42

Then we have the system of equations:

3*G + 7*D = $45

3*G + 6*D = $42

To solve this, we can isolate the term "3*G" in one of the equations (because it appears on both of them)

Let's isolate it on the second equation:

3*G = $42 - 6*D

Now let's replace this on the first equation:

($42 - 6*D) + 7*D = $45

$42 + D = $45

D = $45 - $42 = $3

Then the value of each drugstore coupon is $3.

And we also have the relation:

3*G = $42 - 6*D

We can just replace the value of D to get:

3*G = $42 - 6*$3 = $42 - $24 = $18

G = $18/3 = $6

The value of each grocery store coupon is $6