Respuesta :
Step-by-step 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:
[tex]6j+10w=15.20...(1)[/tex]
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:
[tex]j+2w=2.90...(2)[/tex]
Therefore our system of equations will be:
[tex]6j+10w=15.20...(1)[/tex]
[tex]j+2w=2.90...(2)[/tex]
b. From equation (2) we will get,
[tex]j=2.90-2w[/tex]
Upon substituting this value in equation (1) we will get,
[tex]6(2.90-2w)+10w=15.20[/tex]
Upon distributing 6 we will get,
[tex]17.4-12w+10w=15.20[/tex]
[tex]17.4-2w=15.20[/tex]
[tex]-2w=15.20-17.4[/tex]
[tex]-2w=-2.2[/tex]
[tex]w=\frac{-2.2}{-2}[/tex]
[tex]w=1.1[/tex]
Therefore, the price of each waffle special is $1.1.
Let us substitute w=1.1 in equation (2) to find value of j.
[tex]j+2\times 1.1=2.90[/tex]
[tex]j+2.2=2.90[/tex]
[tex]j=2.90-2.2[/tex]
[tex]j=0.70[/tex]
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.
[tex]\text{The bill for 1 glass of apple juice and 1 waffle}=1.1+0.70[/tex]
[tex]\text{The bill for 1 glass of apple juice and 1 waffle}=1.80[/tex]
Therefore, the amount of bill will be $1.80.
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.
Step-by-step 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
