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04 Aug 2025, 07:32
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Pistachios: 25%
Almonds: 6%
Arman is tracking his fiber intake for the day. His midday snack consists of 200 grams of pistachios, 150 grams of popcorn, and 100 grams of almonds. To meet his nutritional goal, he must consume at least 90 grams of fiber from the snack. The maximum fiber percentages in pistachios, popcorn, and almonds are 27%, 20%, and 10%, respectively.
Select for Pistachios the lowest possible fiber percentage that pistachios can have while still meeting the 90-gram fiber goal, and select for Almonds the lowest possible fiber percentage that almonds can have while still meeting the 90-gram fiber goal. Make only two selections, one in each column.
Select for Pistachios the lowest possible fiber percentage that pistachios can have while still meeting the 90-gram fiber goal, and select for Almonds the lowest possible fiber percentage that almonds can have while still meeting the 90-gram fiber goal. Make only two selections, one in each column.
| Pistachios | Almonds | |
| 0% | ||
| 3% | ||
| 6% | ||
| 20% | ||
| 25% | ||
| 27% |
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Official Answer
Pistachios: 25%
Almonds: 6%
04 Aug 2025, 07:32
Kudos
Bookmarks
Official Solution:
We are given that 200 * P + 150 * C + 100 * A must be greater than or equal to 90, where P, C and A, are fiber percentages in pistachios, popcorn, and almonds, respectively.
200 * P + 150 * C + 100 * A ≥ 90
The maximum fiber percentages are:
Maximum fiber percentage in pistachios = 27%
Maximum fiber percentage popcorn = 20%
Maximum fiber percentage almonds = 10%
General rule for such problems:
To maximize one quantity, minimize the others.
To minimize one quantity, maximize the others.
Minimizing P:
To find the minimum value of P for which 200 * P + 150 * C + 100 * A ≥ 90 holds, we maximize C and A. Using C = 0.20 and A = 0.10, we get:
200 * P + 150 * 0.20 + 100 * 0.10 ≥ 90
200 * P + 30 + 10 ≥ 90
P ≥ 50/200 = 0.25
Thus, the minimum value of P is 25%.
Minimizing A:
To find the minimum value of A for which 200 * P + 150 * C + 100 * A ≥ 90 holds, we maximize P and C. Using P = 0.27 and C = 0.20, we get:
200 * 0.27 + 150 * 0.20 + 100 * A ≥ 90
54 + 30 + 100 * A ≥ 90
A ≥ 6/100 = 0.06
Thus, the minimum value of A is 6%.
Correct answer:
Pistachios "25%"
Almonds "6%"
Bunuel
We are given that 200 * P + 150 * C + 100 * A must be greater than or equal to 90, where P, C and A, are fiber percentages in pistachios, popcorn, and almonds, respectively.
200 * P + 150 * C + 100 * A ≥ 90
The maximum fiber percentages are:
Maximum fiber percentage in pistachios = 27%
Maximum fiber percentage popcorn = 20%
Maximum fiber percentage almonds = 10%
General rule for such problems:
To maximize one quantity, minimize the others.
To minimize one quantity, maximize the others.
Minimizing P:
To find the minimum value of P for which 200 * P + 150 * C + 100 * A ≥ 90 holds, we maximize C and A. Using C = 0.20 and A = 0.10, we get:
200 * P + 150 * 0.20 + 100 * 0.10 ≥ 90
200 * P + 30 + 10 ≥ 90
P ≥ 50/200 = 0.25
Thus, the minimum value of P is 25%.
Minimizing A:
To find the minimum value of A for which 200 * P + 150 * C + 100 * A ≥ 90 holds, we maximize P and C. Using P = 0.27 and C = 0.20, we get:
200 * 0.27 + 150 * 0.20 + 100 * A ≥ 90
54 + 30 + 100 * A ≥ 90
A ≥ 6/100 = 0.06
Thus, the minimum value of A is 6%.
Correct answer:
Pistachios "25%"
Almonds "6%"
