Question

1. As a fundraiser the school is holding a breakfast, the bill for the family special of 6 glasses of apple juice and 10 waffles specials is $15.20, whereas the bill for 1 glass of apple juice and 2 waffles specials is $2.90.

a. Write a system of 2 equations to model this problem. Let j stand for the price of a glass of juice and let w stand for the price of a waffle special.
b. Use the substitution method to solve the system of equations.
c. What would the bill be for 1 glass of apple juice and 1 waffle?

Answer 1

Answer: a) 6 j + 10 w = 15.20, 1 j + 2 w = 2.90 is the required system of the equations.

b) The solution is j = $0.7 and w = $ 1.1

c) $1.8 is the bill be for 1 glass of apple juice and 1 waffle.

Explanation:

Since here j stand for the price of a glass of juice and w stand for the price of a waffle special.

And According to the question,

The bill for the family special of 6 glasses of apple juice and 10 waffles specials is $15.20,

That is, 6 j + 10 w = 15.20 ------ (1)

And, The bill for 1 glass of apple juice and 2 waffles specials is $2.90.

That is, 1 j + 2 w = 2.90 ------ (2)

Since, In substitution method we find the solution by substituting the value of one variable from one equation to other equation,

By equation (2), j = 2.90 - 2 w -----(3)

Put this value of j in equation (1),

We get, 17.4 - 12 w + 10 w = 15.20

⇒ 17.4 - 2 w = 15.20

⇒ 2 w = 2.2

⇒ w = 1.1

Put this value in equation (3),

we get, j = 2.90 - 2×1.1 = 2.90 - 2.2 = 0.7

⇒ j = 0.7

Thus, the cost of one glass of apple juice = $ 0.7

And, the cost of one waffles = $ 1.1

Thus, the bill be for 1 glass of apple juice and 1 waffle = 0.7 + 1.1 = $1.8

Answer 2

Explanation:

Let j be the price of one glass of juice and w br the price of a waffle special.

a. We are told that the bill for the family special of 6 glasses of apple juice and 10 waffles specials is $15.20. We can represent this information as:

`6j+10w=15.20...(1)`

We are also told that the bill for 1 glass of apple juice and 2 waffles specials is $2.90. We can represent this information as:

`j+2w=2.90...(2)`

Therefore our system of equations will be:

`6j+10w=15.20...(1)`

`j+2w=2.90...(2)`

b. From equation (2) we will get,

`j=2.90-2w`

Upon substituting this value in equation (1) we will get,

`6(2.90-2w)+10w=15.20`

Upon distributing 6 we will get,

`17.4-12w+10w=15.20`

`17.4-2w=15.20`

`-2w=15.20-17.4`

`-2w=-2.2`

`w=(-2.2)/(-2)`

`w=1.1`

Therefore, the price of each waffle special is $1.1.

Let us substitute w=1.1 in equation (2) to find value of j.

`j+2* 1.1=2.90`

`j+2.2=2.90`

`j=2.90-2.2`

`j=0.70`

Therefore, the price of each glass of apple juice is $0.70.

c. To find the amount of bill for 1 glass of apple juice and 1 waffle we will add price of 1 waffle special and 1 apple juice.

`\text{The bill for 1 glass of apple juice and 1 waffle}=1.1+0.70`

`\text{The bill for 1 glass of apple juice and 1 waffle}=1.80`

Therefore, the amount of bill will be $1.80.