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Rom4ik [11]
3 years ago
15

Jeremy is making a trail mix containing raisins and peanuts. Raisins cost $1.50 per pound. Peanuts cost $2.50 per pound. Jeremy

spends $10.50 to make 5 pounds of trail mix. He uses the table below to organize this information.
Which equation can Jeremy use to determine the amount of raisins in the trail mix?

a.r + 1.50 = 1.5r
b. r + (5 – r) = 5
c. 1.5r + 2.5(5 – r) = 10.50
d. 1.5r + 2.5(5 – r) = 5

Mathematics
2 answers:
muminat3 years ago
8 0

Answer:

1.5r + 2.5(5 - r) = 10.50

Step-by-step explanation:

Let 'r' is the amount of raisins

Amount of total mixture is 5 pounds

So 5-x is the amount of peanuts

Raisins cost $1.50 per pound. Peanuts cost $2.50 per pound.

1.50(raisins) +2.50(peanuts)= 10.50

Replace raisins with 'r' and peanuts with 5-r

1.5r + 2.5(5 - r) = 10.50

This is our required equation

g100num [7]3 years ago
5 0
1.5r + 2.5(5 - r) = 10.50
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emmainna [20.7K]
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3 years ago
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So for this, we will be using synthetic division. To set it up, have the equation so that the divisor is -10 (since that is the solution of k + 10 = 0) and the dividend are the coefficients. Our equation will look as such:

<em>(Note that synthetic division can only be used when the divisor is a 1st degree binomial)</em>

  • -10 | 1 + 2 - 82 - 28
  • ---------------------------

Now firstly, drop the 1:

  • -10 | 1 + 2 - 82 - 28
  •       ↓
  • -------------------------
  •        1

Next, you are going to multiply -10 and 1, and then combine the product with 2.

  • -10 | 1 + 2 - 82 - 28
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Next, multiply -10 and -8, then combine the product with -82:

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Next, multiply -10 and -2, then combine the product with -28:

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Now, since we know that the degree of the dividend is 3, this means that the degree of the quotient is 2. Using this, the first 3 terms are k^2, k, and the constant, or in this case k² - 8k - 2. Now what about the last coefficient -8? Well this is our remainder, and will be written as -8/(k + 10).

<u>Putting it together, the quotient is k^2-8k-2-\frac{8}{k+10}</u>

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