Question

A small fruit basket with 6 apples and 6 oranges costs $7.50. A different fruit basket with 10 apples and 5 oranges costs $8.75. If x is the cost of one apple and y is the cost of one orange, the system of equations below can be used to determine the cost of one apple and one orange. 6x+6y=7.50 10x+5y=8.75

Answer 1

Answer:

x = $0.50

y= $0.75

Step-by-step explanation:

1. Multiply the equations to have the same coefficients

5(6x + 6y = 7.5) → 30x + 30y = 37.5

3(10x + 5y = 8.75) → 30x + 15y = 26.25

2. Subtract the equations

 30x + 30y = 37.5

- 30x + 15y = 26.25

15y = 11.25

3. Solve for y by dividing both sides by 15

y = 0.75

4. Plug in 0.75 for y into one of the equations

6x + 6(0.75) = 7.5

5. Simplify

6x + 4.5 = 7.5

6. Solve for x

6x = 3

x = 0.5

Answer 2

Answer:

The cost of one apple is $0.5

The cost of one orange is $0.75

Step-by-step explanation:

Given information

The cost of an apple = $x$

The cost of an orange = $y$

Equation to find the values are:

$6x=6y=7.50\\10x+5y=8.75$

Now, convert the equations to have same coefficient as:

$5(6x=6y=7.50)\\=30x+30y=37.5\\3(10x+5y=8.75)\\=30x+15y=26.25$

Now, on solving the above equation by subtracting one from another.

We get,

$15y=11.25\\y=0.75$

Now , put the value of $y$ in one equation to find the value of $x$.

As,

$6x+4.5=7.5\\x=0.5$

Hence,

The cost of one apple is $0.5

The cost of one orange is $0.75

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