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, fast!
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To find the weight of 2 grapefruits and 8 plums, we need to first determine the weight of a single grapefruit and a single plum.
We are given that one grapefruit weighs the same as 3 plums. Let's assign variables to represent the weight of a grapefruit and a plum.
Let's call the weight of a grapefruit "g" and the weight of a plum "p".
According to the given information, we have two equations:
1) g = 3p (one grapefruit weighs the same as 3 plums)
2) 10g + 20p = 175 (the total weight of the 10 grapefruits and 20 plums is 175 ounces)
Now, let's solve the system of equations to find the weight of a single grapefruit (g) and a single plum (p):
Substitute equation 1) into equation 2):
10(3p) + 20p = 175
30p + 20p = 175
50p = 175
p = 3.5
Now we know that the weight of a single plum is 3.5 ounces.
Substitute the value of p back into equation 1) to find the weight of a single grapefruit (g):
g = 3(3.5)
g = 10.5
Therefore, the weight of a single grapefruit is 10.5 ounces.
Now, let's find the weight of 2 grapefruits and 8 plums:
2 grapefruits weigh: 2(10.5) = 21 ounces
8 plums weigh: 8(3.5) = 28 ounces
Therefore, the total weight of 2 grapefruits and 8 plums is 21 + 28 = 49 ounces.