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gia57
29.10.2020 •
Mathematics
A farmer's market sells pecans, walnuts, and cashews. They each have a different cost and are priced per pound. Alyssa buys five pounds of walnuts and seven pounds of cashews and spends $75. Landon buys two pounds of pecans and three pounds of walnuts and spends $31. Tina buys 4 pounds of pecans and 3 pounds of cashews and spends $29. Find the missing quantity below. Price per pound for Walnuts = $
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Ответ:
price per pound of walnut = x = $8
price per pound of pecans = y = $3.5
price per pound of cashew = z = $5
Step-by-step explanation:
Let
price per pound of walnut = x price per pound of pecans = y price per pound of cashew = z.
Alyssa;
5x + 7z = 75
Landon:
2y + 3x = 31
Tina:
4y + 3z = 29
5x + 7z = 75 (1)
2y + 3x = 31 (2)
4y + 3z = 29 (3)
From (1)
5x + 7z = 75
5x = 75 - 7z
x = (75 - 7z) / 5
Substitute x = (75 - 7z) / 5 into (2)
2y + 3x = 31
2y + 3((75 - 7z) / 5 = 31
2y + (225 - 21z) /5 = 31
(225 - 21z) /5 = 31 - 2y
225 - 21z = 5(31 - 2y)
225 - 21z = 155 - 10y
225 - 155 = -10y + 21z
70 = -10y + 21z
-10y + 21z = 70
4y + 3z = 29 (3)
-10y + 21z = 70 (4)
Multiply (3) by 7
28y + 21z = 203. (3b)
-10y + 21z = 70 (4)
Subtract (4) from (3b)
28y - (-10y) = 203 - 70
28y + 10y = 133
38y = 133
y = 133/38
= 3.5
y = 3.5
Substitute y = 3.5 into (3)
4y + 3z = 29 (3)
4(3.5) + 3z = 29
14 + 3z = 29
3z = 29 - 14
3z = 15
z = 15/3
z = 5
Substitute z = 5 into (1)
5x + 7z = 75 (1)
5x + 7(5) = 75
5x + 35 = 75
5x = 75 - 35
5x = 40
x = 40/5
x = 8
price per pound of walnut = x = $8
price per pound of pecans = y = $3.5
price per pound of cashew = z = $5
Ответ:
Price per pound for Walnut is $8
Step-by-step explanation:
Represent Walnuts with W, Pecans with P and Cashew with C
For Alyssa:
For Landon:
For Tina:
Required
Solve for W
Considering the last equation, make P the subject:
Substitute this expression for P in the second equation
Multiply through by 2
Make C the subject
Substitute this in the first equation
Price per pound for Walnut is $8
Ответ:
x=B/7-6/7
Step-by-step explanation: