Wilma went to the local market and bought 3 lemons and 5 oranges for $2.40.The same day and for the same price ,Fran bought 4 lemons and 7 oranges for $3.31.What was the prices per lemon and the price per orange?
3L + 5O = 2.40
4L + 7O = 3.31
Multiply fist equation by 4 and second by 3, then subtract one from the other. Insert the orange price into one of the equations to find the lemon price.
To find the price per lemon and the price per orange, we can set up a system of equations based on the information given:
Let's assume the price per lemon is L and the price per orange is O.
According to the information given, we can create the following equations:
1. 3L + 5O = 2.40 (Equation 1) - This equation represents the total cost of 3 lemons and 5 oranges purchased by Wilma.
2. 4L + 7O = 3.31 (Equation 2) - This equation represents the total cost of 4 lemons and 7 oranges purchased by Fran.
We can solve this system of equations to find the values of L and O.
Let's solve this system using the method of substitution:
From Equation 1, we can express L in terms of O:
3L = 2.40 - 5O (Equation 3)
L = (2.40 - 5O) / 3 (Equation 4)
Substitute Equation 4 into Equation 2:
4[(2.40 - 5O) / 3] + 7O = 3.31
Multiply both sides of the equation by 3 to eliminate the fraction:
4(2.40 - 5O) + 21O = 9.93
9.60 - 20O + 21O = 9.93
9.60 + O = 9.93
O = 9.93 - 9.60
O = 0.33
Now, substitute the value of O back into Equation 4 to find L:
L = (2.40 - 5(0.33)) / 3
L = (2.40 - 1.65) / 3
L = 0.75 / 3
L = 0.25
Therefore, the price per lemon is $0.25 and the price per orange is $0.33.