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MakcuM [25]
3 years ago
12

Sarah's Shipping and Ryan's Mail Services both ship packages. Sarah's trucks will only carry loads of 18 packages. In contrast,

Ryan's trucks will only carry loads of 11 packages. If both businesses end up shipping the same number of packages this morning, what is the minimum number of packages each must have shipped?
Mathematics
2 answers:
Lorico [155]3 years ago
4 0
Easy 18 - 11 = 7 ............................................

Sauron [17]3 years ago
4 0

Answer:

The minimum number of packages each must have shipped is 198.

Step-by-step explanation:

Sarah's trucks will only carry loads of 18 packages.

Ryan's trucks will only carry loads of 11 packages.

To find the minimum number of packages each must have shipped, we will find the LCM.

18 = 2 x 3 x 3

11 = 11 x 1

LCM = 18 x 11 = 198

Hence, the minimum number of packages each must have shipped is 198.

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A home gardener estimates that 24 apple trees will have an average yield of 104 apples per tree. But because of the size of the
d1i1m1o1n [39]

Answer:

The farmer should plant 14 additional trees, for maximum yield.

Step-by-step explanation:

Given

Trees = 24

Yield = 104

x \to additional\ trees

So, we have:

Trees = 24 + x

Yield = 104 - 2x

Required

The additional trees to be planted for maximum yield

The function is:

f(x) = Trees * Yield

f(x) = (24 + x) * (104 - 2x)

Open bracket

f(x) = 24 * 104 + 104x - 24 * 2x - x * 2x

f(x) = 2796 + 104x - 48x - 2x^2

f(x) = 2796 + 56x - 2x^2

Rewrite as:

f(x) = - 2x^2 + 56x + 2796

Differentiate

f'(x) = -4x + 56

Equate f'(x) = -4x + 56 to 0 and solve for x to get the maximum of x

-4x + 56 = 0

-4x =- 56

Divide by -4

x =14

The farmer should plant 14 additional trees, for maximum yield.

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