mary went to the store for some fruit. The apples were $1.00 per pound and the oranges were $0.50 per poumd. She spent $5,00 all together and took home a total of 8 pond of fruit. How many ponds of apples and oranges did she buy?
Let O and A stand for pounds of fruit.
O + A = 8
A = 8 - O
.5O + A = 5
Substitute 8-O for A in third equation and solve for O. Insert that value into the first equation and solve for A. Check by inserting both values into the third equation.
To solve this problem, we need to set up a system of equations based on the given information.
Let's assume Mary bought x pounds of apples and y pounds of oranges.
According to the problem, the cost of apples is $1.00 per pound, so the equation for the cost of apples would be: 1x.
Similarly, the cost of oranges is $0.50 per pound, so the equation for the cost of oranges would be: 0.50y.
The total cost of the fruit is $5.00, so the equation for the total cost would be: 1x + 0.50y = 5.00.
We also know that Mary bought a total of 8 pounds of fruit, so the equation for the total weight would be: x + y = 8.
We now have a system of two equations:
1x + 0.50y = 5.00 (Equation 1)
x + y = 8 (Equation 2)
To solve this system of equations, we can use various methods like substitution or elimination. Let's use the elimination method.
Multiply Equation 2 by 0.50 to make the coefficients of y in both equations the same:
0.50(x + y) = 0.50(8)
0.50x + 0.50y = 4 (Equation 3)
Now, subtract Equation 3 from Equation 1 to eliminate the y variable:
(1x + 0.50y) - (0.50x + 0.50y) = 5.00 - 4.00
This simplifies to:
0.50x = 1.00
Divide both sides of the equation by 0.50:
x = 2
Now substitute the value of x into Equation 2:
2 + y = 8
Subtract 2 from both sides of the equation:
y = 6
Therefore, Mary bought 2 pounds of apples and 6 pounds of oranges.