Question

Gabriella went to the grocery store and bought bottles of soda and bottles of juice. Each bottle of soda has 45 grams of sugar, and each bottle of juice has 30 grams of sugar. Gabriella purchased 3 more bottles of juice than bottles of soda, and they all collectively contain 540 grams of sugar. Graphically solve a system of equations to determine the number of bottles of soda purchased (x) and the number of bottles of juice purchased (y).

A) x = 6, y = 9
B) x = 8, y = 11
C) x = 12, y = 15
D) x = 15, y = 18

Answer 1

Gabriella purchased 6 bottles of soda and 9 bottles of juice as determined by graphically solving the system of equations 45x + 30(x + 3) = 540 and y = x + 3.

Step-by-step explanation:

To determine the number of bottles of soda (x) and bottles of juice (y) Gabriella purchased, we can set up a system of equations based on the information given:

• Each bottle of soda has 45 grams of sugar.
• Each bottle of juice has 30 grams of sugar.
• Gabriella purchased 3 more bottles of juice than bottles of soda.
• The total amount of sugar is 540 grams.

The two equations representing this situation are:

1. y = x + 3 (3 more bottles of juice than soda)
2. 45x + 30y = 540 (total sugar amount)

Substitute equation (1) into equation (2) to solve graphically:

45x + 30(x + 3) = 540

Simplify and solve for x:

45x + 30x + 90 = 540

75x + 90 = 540

75x = 540 - 90

75x = 450

x = 450 / 75

x = 6

Now solve for y using equation (1):

y = 6 + 3

y = 9

Thus, Gabriella purchased 6 bottles of soda and 9 bottles of juice.

The correct answer is:

A) x = 6, y = 9