Respuesta :
Answer:
x = 4 pounds.
Step-by-step explanation:
Let x be the mix amount of $1.5
Be and the amount of mixture of $0.8
Let z be the amount of mix of $1
We know that an amount x of mix of $ 1.5 should be added to y = 10 pounds of mix of $ 0.8 to get mix of $ 1. This is
x + y = z
x +10 = z (i)
Then, we know that the amount of money invested in the mix must be:
1.5x + 0.8y = 1z (ii)
We must clear x.
For this we substitute (i) in (ii)
1.5x + 0.8y = x + 10
-10 + 0.8y = = -0.5x
We know that y = 10.
So:
0.5x = 10 - 0.8(10)
x = 2(10-8)
x = 4 pounds.
You must add 4 pounds of 1.5 $ mix
[tex]\boxed{4{\text{ pounds}}}[/tex] of chocolate worth [tex]\$1.5[/tex] a pound must be mixed with 10 pounds of chocolate worth 80 cents a pound to produce a mixture worth [tex]\$1[/tex] a pound.
Further explanation:
Given:
The cost of 10 pounds of chocolate is 80 cents.
Explanation:
Consider the amount of chocolate worth [tex]\$1.5[/tex] a pound be [tex]x{\text{ pounds}}.[/tex]
The cost of 10 pounds of chocolate that worth 80 cents a pound can be obtained as follows,
[tex]\begin{aligned}{\text{Cost}} &= 0.8 \times 10\\&= \$ 8\\\end{aligned}[/tex]
The amount of chocolate worth [tex]\$1.5[/tex] a pound can be obtained as follows,
[tex]\begin{aligned}1.5x + 8 &= x + 10\\ 1.5 - x &= 10 - 8 \\ 0.5x &=2\\x&= \frac{2}{{0.5}}\\x&= \frac{{20}}{5}\\x &= 4\\\end{aligned}[/tex]
[tex]\boxed{4{\text{ pounds}}}[/tex] of chocolate worth [tex]\$1.5[/tex] a pound must be mixed with 10 pounds of chocolate worth 80 cents a pound to produce a mixture worth [tex]\$1[/tex] a pound.
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Answer details:
Grade: High school
Subject: Mathematics
Chapter: Number system
Keywords: pounds, chocolate, worth, 10 pounds, mixture, produced, $1 a pound, one pound, mixed, 80 cents, 80 cents a pound.
