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Pepsi [2]
3 years ago
14

In a basketball game Fintan made 16 baskets. Each of the baskets is worth either 2 or 3

Mathematics
1 answer:
jekas [21]3 years ago
8 0
Let x represent a 2-point basket, and y represent a 3-point basket.

Basket equation: x + y = 16
Point equation 2x + 3y = 39

Solve using system of equations:
if x + y = 16, then x = 16 - y

Plug into the second equation:
2(16-y) + 3y = 39
32 - 2y + 3y = 39
32 + y = 39
y = 7

So the number of 3-point baskets scored was 7. Hope this helps, let me know if there’s a step you don’t understand! :)
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A ladder is leaning against a building. The distance from the bottom of the ladder to the building is 16 ft less than the length
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Let's say the length of the ladder is "d". Since the distance from the bottom of the ladder to the building is 16 feet less than the length, we can write this as d - 16.

The distance from the ground to the top of the ladder is 2 feet less than the length of the ladder, so we can denote this as

d - 2.

The shape made by the ground, ladder, and side of the building is a right triangle, and we just found its legs. We can use the Pythagorean Theorem to solve for "d" and find how far up the side of the building the ladder is:

(d - 16)^2 + (d - 2)^2 = d^2

(d^2 - 32d + 256) + (d^2 - 4d + 4) = d^2

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(d - 26) * (d - 10) = 0

d = 26 or d = 10

The answer d = 10 does not fit in this case because it isn't possible to have 16 feet less of 10 feet; it would be negative!

So, d = 26. The top of the ladder to the ground is 2 less than d, so we do 26 - 2 = 24 feet.

The answer is 24 feet.

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