Mrs. Porter purchased 10 grapefruit and 20 plums. One grapefruit weighs the same as 3 plums. The weight of all 30 pieces of fruit is 175 ounces. The total weight of 2 grapefruits and 8 plums is (blank) ounces. Please help.
You are told that
g = 3p
10g+20p=175
so,
10*3p + 20p = 175
50p = 175
p = 7/2
g = 3p = 21/2
2g+8p = 2(7/2)+8(21/2) = 88
Thanks again
Let's break down the problem step-by-step:
Step 1: Assign variables
Let's assign variables to the unknown quantities in the problem:
- Let's call the weight of one grapefruit "g" (in ounces).
- Let's call the weight of one plum "p" (in ounces).
Step 2: Set up equations
From the given information, we can set up two equations:
- Equation 1: 10g + 20p = 175 (since the total weight of all 30 pieces of fruit is 175 ounces)
- Equation 2: g = 3p (since one grapefruit weighs the same as 3 plums)
Step 3: Solve the equations
Substitute the value of "g" from Equation 2 into Equation 1:
10(3p) + 20p = 175
30p + 20p = 175
50p = 175
p = 175/50
p = 3.5
Now substitute the value of "p" into Equation 2 to find the weight of one grapefruit:
g = 3(3.5)
g = 10.5
Step 4: Calculate the total weight of 2 grapefruits and 8 plums
To find the total weight of 2 grapefruits and 8 plums, we need to multiply the weight of one grapefruit by 2 and the weight of one plum by 8, then add them together:
Total weight = (2 * 10.5) + (8 * 3.5)
Total weight = 21 + 28
Total weight = 49 ounces
Therefore, the total weight of 2 grapefruits and 8 plums is 49 ounces.
To find the total weight of 2 grapefruits and 8 plums, we need to determine the weight of one grapefruit and one plum first.
Let's assume the weight of one grapefruit is G ounces and the weight of one plum is P ounces. According to the given information, one grapefruit weighs the same as 3 plums. So, we can write the equation:
G = 3P
Now, let's calculate the total weight of all 30 pieces of fruit. We know that Mrs. Porter purchased 10 grapefruits and 20 plums, which makes a total of 30 pieces. The total weight is given as 175 ounces. This can be expressed as:
10G + 20P = 175
Now, we have a system of two equations:
G = 3P (equation 1)
10G + 20P = 175 (equation 2)
To solve this system, we'll use the substitution method.
Step 1: Solve equation 1 for G in terms of P.
G = 3P
Step 2: Substitute G in equation 2 with 3P.
10(3P) + 20P = 175
30P + 20P = 175
50P = 175
P = 3.5
Step 3: Calculate the value of G using equation 1.
G = 3P
G = 3(3.5)
G = 10.5
Step 4: Calculate the total weight of 2 grapefruits and 8 plums.
Total weight = (2G) + (8P)
Total weight = (2 * 10.5) + (8 * 3.5)
Total weight = 21 + 28
Total weight = 49 ounces
Therefore, the total weight of 2 grapefruits and 8 plums is 49 ounces.