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ivanzaharov [21]
3 years ago
8

A store is mixing up two types of nuts, peanuts and cashews into a 50 lb barrel. peanuts sell for $4 a pound and cashews sell fo

r $7 a pound. If the store wants to sell the mix for $5.75 a pound, how many pounds of each nut should be put into the mix?
Mathematics
1 answer:
Zielflug [23.3K]3 years ago
4 0

Answer:

Cashew 12.5lb

Peanuts 37.5lb

Step-by-step explanation:

Let the number of pounds of cashewnuts and peanuts be c and p respectively.

Firstly, the total mass of the nuts is 50.

This means:

c + p = 50

Now let’s work with the money

4p + 7c = 4.75(50)

From the first equation, let c = 50 - p

Substitute this into the second equation.

4p + 7(50 - p) = 237.5

4p + 350 - 7p = 237.5

3p = 112.5

P = 112.5/3 = 37.5lb

For Cashew c = 50 - p = 50 - 37.5 = 12.5lb

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Find an equation for the nth term of the arithmetic sequence.
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Answer:

The equation of the nth term is an = -621 + 42n

Step-by-step explanation:

* Lets revise the arithmetic sequence

- There is a constant difference between each two consecutive numbers

- Ex:

# 2  ,  5  ,  8  ,  11  ,  ……………………….

# 5  ,  10  ,  15  ,  20  ,  …………………………

# 12  ,  10  ,  8  ,  6  ,  ……………………………

* General term (nth term) of an Arithmetic sequence:

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- Un = a + (n – 1)d, where a is the first term , d is the difference

  between each two consecutive terms

, n is the position of the term

* Lets solve the problem

∵ an = a + (n - 1)d

∴ a14 = a + (14 - 1)d

∴ a14 = a + 13d

∵ a14 = -33

∴ a + 13d = -33 ⇒ (1)

- Similar we can find another equation from a15

∵ a15 = a + (15 - 1)d

∴ a15 = a + 14d

∵ a15 = 9

∴ a + 14d = 9 ⇒ (2)

- We will solve equations (1) and (2) to find a and d

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∴ -d = -42 ⇒ × both sides by -1

∴ d = 42

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∴ an = -621 + 42n

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