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azamat
3 years ago
7

Cherries $5 per pound and oranges per pound$2. He paid 18.00 for total weight which was 6 lbs how many pounds of cherries did Al

ex buy
Mathematics
1 answer:
wel3 years ago
5 0
Answer: 2 lbs of cherries

Cherries = $5 per pound
Oranges = $2 per pound
Total Cost = $18
Total weight = 6 lb

------------------------------------
Define x and y
------------------------------------
Let x be the number of lb of cherries
Let y be the number of lb of oranges

------------------------------------
Construct equations
------------------------------------
x + y = 6               ---------------------------- (1)
5x + 2y = 18         ---------------------------- (2)

------------------------------------------------------------------------
Solve x and y
------------------------------------------------------------------------
From equation (1):
x + y = 6 
x = 6 - y 

------------------------------------------------------------------------
Substitute x = 6 - y into equation 2
------------------------------------------------------------------------
5x + 2y = 18
5 (6 - y) + 2y = 18
30 - 5y + 2y = 18
3y = 30 - 18
3y = 12
y = 4

------------------------------------------------------------------------
Substitute y = 4 into equation (1)
------------------------------------------------------------------------
x + y = 6
x + 4 = 6
x = 2

------------------------------------------------------------------------
Find the weight of cherries and oranges
------------------------------------------------------------------------
Cherry = x = 2 lb
Oranges = y = 4 lbs 

------------------------------------------------------------------------
Answer: Alex bought 2 lb of cherries
------------------------------------------------------------------------
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Q1  Solution:

x = 3 or x = -1

Step-by-step explanation:

x²-2x-3 = 0

In order to solve the quadratic equation by factoring, we have to determine two numbers whose sum is -2 and their product -3. By trial and error the two numbers are found to be; -3 and 1. The next step is to split the middle term by substituting it with the above two numbers found;

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x-3= 0 or x+1 = 0

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Q2  Solution:

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Step-by-step explanation:

2x²-5x-3  =0

In order to solve the quadratic equation by factoring, we have to determine two numbers whose sum is -5 and their product 2(-3)=-6. By trial and error the two numbers are found to be; -6 and 1. The next step is to split the middle term by substituting it with the above two numbers found;

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Q3 Soution:

x = 4 or x = 3

Step-by-step explanation:

x²-7x = -12

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x(x-4)-3(x-4)  = 0

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Q4:

x = -2/3 or x = 6

Step-by-step explanation:

3x² = 16x+12

3x²-16x-12 = 0

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Q5:

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Step-by-step explanation:

x²-2x-24 = 0

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Q6:

x  = 4/3 or x  = -1

Step-by-step explanation:

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Step-by-step explanation:

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