At her juice parlor, Mrs. Jones makes a different amount of fruit punch each day by mixing grape juice and peach juice. The tabl
e shows the amount of grape juice, g, and the amount of peach juice, p, Mrs. Jones uses to make different quantities of the punch. Which equation represents the proportional relationship between the amounts of grape juice and peach juice?
2 answers:
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Answer:
Question 1) 6x+5
Question 2) Blank #1: sum. Blank #2: 5. Blank #3: 4
See work in the attachment. If you're still confused, read the step-by-step explanation for a more in-depth explanation of what exactly I did for my work. Let me know if you have any questions :>
Step-by-step explanation:
For question 1, it's important to know that the perimeter is equal to the sum of all the sides. Since the shape is a rectangle, the sides opposite of each other are the same length. Thus, the left and right sides are both 3x - 3. 2(3x - 3) = 6x - 6. The unknown value, which I called a, is the same for both the top and the bottom. To find it, you must first subtract 6x - 6 from the perimeter of 18x + 4. This equals 12x + 10. Then, divide that answer by 2 to get the unknown side. You then get 6x + 5 as the answer for the unknown side.
To make sure it's correct, you can plug in a random number for x. In this case, I checked my work by plugging 2 in for x.
Perimeter = 18(2) + 4 = 36 + 4 = 40
Perimeter = 6(2) + 5 + 6(2) + 5 + 3(2) - 3 + 3(2) - 3 = 12 + 5 + 12 + 5 + 6 - 3 + 6 - 3 = 24 + 10 + 12 - 6 = 40
For question 2, the main idea you need to know is that A = lw. The area of the first rectangle is 6 * 5 = 30. The area of the second rectangle is 6 * 4 = 24. When you add them together, you get 54. The area of the rectangle that is formed when you combine rectangle 1 and rectangle 2 is 6 * 9 = 54. This shows that 6(4) + 6(5) = 6(9)
