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Margarita [4]
3 years ago
5

One week Beth bought 3 apples and 8 pears for $14.50. The next week she bought 6 apples and 4 pears and paid $14. Find the cost

of 2 apple and the cost of 1 pear.
Mathematics
1 answer:
zalisa [80]3 years ago
5 0
Let us assume the cost of 1 apple = x dollars
Let us also assume the cost of 1 pear = y dollars
Then we can form two equations from the details given in the question. Based on those details the required answer to the question can be easily deduced.
3x + 8y = 14.50
And
6x + 4y = 14
Dividing both sides of the equation by 2 we get
3x + 2y = 7
2y = 7 - 3x
y = (7 - 3x)/2
Putting the value of y from the second equation in the first equation we get
3x + 8y = 14.50
3x + 8[(7 - 3x)/2] = 14.50
3x + 4 (7 - 3x) = 14.50
3x + 28 - 12x = 14.50
- 9x = 14.50 - 28
- 9x = - 13.5
9x = 13.5
x = 13.5/9
   = 1.5
Putting the value of x in the second equation we get
6x + 4y = 14
(6 * 1.5) + 4y = 14
9 + 4y = 14
4y = 14 - 9
4y = 5
y = 5/4
   = 1.25
So we can find from the above deduction that the cost of 1 apple is 1.5 dollars and the cost of 1 pear is 1.25 dollars
Then
Cost of 2 apples = 2 * 1.5 dollars
                           = 3.0 dollars
So the cost of 2 apples is $3 and the cost of 1 pear is $1.25.
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Answer:

 x = -2/5

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Step-by-step explanation:

Substitution method;

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       y = 12/5

elimination method:

-2x + 3y = 8  -----------(i)

x + y =2   -----------(ii)

                                    (i)   ====>    -2x + 3y = 8

multiply equ (ii) by 2         ====>    <u>  2x + 2y = 4</u>

             add (i) and (ii)                             5y = 12

                                                                   y = 12/5

Substitute in equ (ii)

x + 12/5 = 2

        x = 2 - 12/5

           = 2*5/1*5 - 12/5  

          = 10 -12/5 = -2/5

Ans: x = -2/5

       y = 12/5

                                                       

               

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