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Sindrei [870]
2 years ago
5

1. Enrico sold a 10-pound box of assorted chocolates. Some of the chocolates in the box sold

Mathematics
1 answer:
N76 [4]2 years ago
6 0

This shows that about 7 and 3 pounds of each chocolate were included in the mixture.

Let the number of pounds of both chocolates be x and y.

If Enrico sold a 10-pound box of assorted chocolates, hence;

x + y = 10 ................. 1

If some of the chocolates in the box sold  for $1.75 per pound and some sold for $2.00 per pound with mixture sold for $1.90 per pound, then:

1.75x + 2x = 1.90 ................ 2

Solve equations 1 and 2 simultaneously.

x + y = 10 ................. 1 * 20

17.5x + 20x = 19 ................ 2 * 1

____________________________

20x + 20y = 200

17.5x + 20x = 19

Subtract

20x - 17.5x = 200 - 19

2.5x = 181x = 7.24

Substitute 7.24 into 1

x  + y = 10

y = 10 - 7.24

x = 2.76

This shows that about 7 and 3 pounds of each chocolate were included in the mixture.

Learn more here: brainly.com/question/15165519

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Answer:

  • CDs — $10,000
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  • stocks — $45,000

Step-by-step explanation:

Let the variables c, b, s represent the dollar amounts invested in CDs, stocks, and bonds, respectively. Then the problem statement gives us 3 relations between these 3 variables:

  c + b + s = 135000 . . . . . . . . . . . . . . . . . total invested

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  -c + b = 70000 . . . . . . . . . . . . . . . . . . . . . 70,000 more was in bonds than CDs

Using the third equation to write an expression for b, we can substitute into the other two equations.

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  c + (70000 +c) +s = 135000 . . . . substitute for b in the first equation

  2c +s = 65000 . . . . . . . . . . . . . . . . [eq4] simplify

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  .0725c +.104s = 5405 . . . . . . . . . . [eq5] simplify

Using [eq4], we can write an expression for s that can be substituted into [eq5].

  s = 65000 -2c . . . . . . . expression we can substitute for s

  0.0725c +0.104(65000 -2c) = 5405

  -0.1355c = -1355 . . . . . . . . . . . . . . . . . . . . subtract 6760, simplify

  c = 1355/.1355 = 10,000

  s = 65000 -2×10000 = 45,000

  b = 70000 +10000 = 80,000

The amounts invested in stocks, bonds, and CDs were $45,000, $80,000, and $10,000, respectively.

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Alternatively, you can reduce the augmented matrix for this problem to row-echelon form using any of several calculators or on-line sites. That matrix is ...

\left[\begin{array}{ccc|c}1&1&1&135000\\0.0275&0.045&0.104&8555\\-1&1&0&70000\end{array}\right]

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