4 oranges and 6 grapefruit cost $2.62. 7 oranges and 5 grapefruit sell for $2.66. What is the cost of 1 grapefruit, and 1 orange?

help me guys

4O + 6G = 2.62

7O + 5G = 2.66

Multiply first equation by 5 and second by 6.

20O + 30G = 13.10

42O + 30G = 15.96

Subtract first equation from second.

22O = 2.86

O = .13

Take it from there.

To find the cost of one grapefruit and one orange, we can set up a system of equations based on the given information.

Let's assume the cost of one orange is represented by "x" and the cost of one grapefruit is represented by "y".

From the first statement, we know that 4 oranges and 6 grapefruit cost $2.62, so we can write the equation:

4x + 6y = 2.62

From the second statement, we know that 7 oranges and 5 grapefruit sell for $2.66, so we can write another equation:

7x + 5y = 2.66

Now, we can solve this system of equations. There are several methods to solve it, but let's use the method of substitution.

1. Solving for x in terms of y:
From the first equation, isolate x:
4x = 2.62 - 6y
x = (2.62 - 6y) / 4

2. Substitute this value of x into the second equation:
7[(2.62 - 6y) / 4] + 5y = 2.66

Simplify the equation:
(2.62 - 6y) + (5y * 4) = 2.66 * 4
2.62 - 6y + 20y = 10.64

Combine like terms:
14y = 10.64 - 2.62
14y = 8.02

Divide by 14 to solve for y:
y = 8.02 / 14
y = 0.573

So, the cost of one grapefruit is $0.573.

To find the cost of one orange, substitute this value of y back into the first equation:

4x + 6(0.573) = 2.62
4x + 3.438 = 2.62
4x = 2.62 - 3.438
4x = -0.818
x = -0.818 / 4
x = -0.2045

However, since the cost cannot be negative, we need to consider that there might be an error in the problem or the information provided. Please double-check the given details or consult with the original source for clarification.