Sue has red apples worth 2.30$ per pound and green apples worth 1.90$ a pound How many pounds of each should she mix to get a mixture of 20 pounds worth 2.06$ per pound?

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Sue has red apples worth 2.30$ per pound and green apples worth 1.90$ a pound How many pounds of each should she mix to get a mixture of 20 pounds worth 2.06$ per pound?

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Answer 1 · 2017-10-22T01:30:02

8 pounds of red apples
12 pounds of green apples

Explanation:

The "pounds" is the variable with different cost factors.
The total package of 20 pounds will have a value of
$20 \times 2.06 = 41.20$ $20 xx 2.06 = 41.20$

The components of this value are from the two apple types:
$41.20 = 2.30 \times W_{r} + 1.90 \times W_{g}$ $41.20 = 2.30 xx W_r + 1.90 xx W_g$
$W_{r} + W_{g} = 20$ $W_r + W_g = 20$ ; $W_{r} = 20 - W_{g}$ $W_r = 20 - W_g$

Substitute this into the overall equation:
$41.20 = 2.30 \times (20 - W_{g}) + 1.90 \times W_{g}$ $41.20 = 2.30 xx (20 - W_g) + 1.90 xx W_g$

Solve for $W_{g}$ $W_g$ :
$41.20 = 46 - 2.30 \times W_{g} + 1.90 \times W_{g}$ $41.20 = 46 - 2.30 xx W_g + 1.90 xx W_g$
$- 4.80 = - 0.4 \times W_{g}$ $-4.80 = -0.4 xx W_g$ ; $W_{g} = 12$ $W_g = 12$

Solve for $W_{r}$ $W_r$ :
$W_{r} = 20 - W_{g}$ $W_r = 20 - W_g$ ; $W_{r} = 20 - 12 = 8$ $W_r = 20 - 12 = 8$

CHECK:
$41.20 = 2.30 \times W_{r} + 1.90 \times W_{g}$ $41.20 = 2.30 xx W_r + 1.90 xx W_g$
$41.20 = 2.30 \times 8 + 1.90 \times 12$ $41.20 = 2.30 xx 8 + 1.90 xx 12$
$41.20 = 18.40 + 22.80 = 41.20$ $41.20 = 18.40 + 22.80 = 41.20$ CORRECT!

Answer 2 · 2017-10-22T01:32:54

Red apples $= 8$ $=8$ pounds
Green apples $= 12$ $=12$ pounds

Explanation:

Let Red Apples, bought be $x$ $x$ pounds
Let Green Apples, bought be $y$ $y$ pounds

Then-

$x + y = 20$ $x + y = 20$ in terms of quantity --------------- (1)
$(x \times 2.30) + (y \times 1.90) = 20 \times 2.06$ $(x xx 2.30) +(y xx 1.90) =20 xx 2.06$ in terms of money

$2.3 x + 1.9 y = 41.2$ $2.3x+1.9y=41.2$ ------------ (2)

Solve equation (1) for $x$ $x$

$x = 20 - y$ $x=20-y$

Substitute $x = 20 - y$ $x=20-y$ in equation (2)

$2.3 (20 - y) + 1.9 y = 41.2$ $2.3(20-y)+1.9y=41.2$
$46 - 2.3 y + 1.9 y = 41.2$ $46-2.3y+1.9y=41.2$
$- 0.4 y = 41.2 - 46 = - 4.8$ $-0.4y=41.2-46=-4.8$
$y = \frac{- 4.8}{- 0.4} = 12$ $y=(-4.8)/(-0.4)=12$

$y = 12$ $y= 12$
Substitute $y = 12$ $y= 12$ in equation (1)

$x + 12 = 20$ $x+12=20$
$x = 20 - 12 = 8$ $x=20-12=8$
$x = 8$ $x=8$

Red apples $= 8$ $=8$ pounds
Green apples $= 12$ $=12$ pounds

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Sue has red apples worth 2.30$ per pound and green apples worth 1.90$ a pound How many pounds of each should she mix to get a mixture of 20 pounds worth 2.06$ per pound?

2 Answers

Explanation:

Explanation:

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