Two apples and three pears cost $3.45. Three apples and five pears cost $5.55. Find the cost of each type of fruit.
a = apples
p = pears
Two equations
2a + 3p = 345
3a + 5p = 555
Elimination Method
3(2a + 3p = 345)
-2(3a + 5p = 555)
6a + 9p = 1035
-6a - 10p = -1110
________________________
-p = -75
p = 75
2a + 3(75)= 345
2a + 225 = 345
2a = 345 - 225
2a = 120
2a/2 = 120/2
a = 60
To solve this problem, we can set up a system of equations.
Let a be the cost of one apple and p be the cost of one pear.
From the given information, we can write the following equations:
Equation 1: 2a + 3p = 3.45 (two apples and three pears cost $3.45)
Equation 2: 3a + 5p = 5.55 (three apples and five pears cost $5.55)
To find the cost of each type of fruit, we need to solve this system of equations.
One way to solve this is by using the method of elimination.
Multiplying Equation 1 by 3 and Equation 2 by 2, we get:
6a + 9p = 10.35 (3 times Equation 1)
6a + 10p = 11.1 (2 times Equation 2)
Now, we can subtract Equation 1 from Equation 2:
(6a + 10p) - (6a + 9p) = 11.1 - 10.35
6a - 6a + 10p - 9p = 0.75
p = 0.75
Now that we have the value of p, we can substitute it into either of the original equations to find the value of a.
Using Equation 1:
2a + 3(0.75) = 3.45
2a + 2.25 = 3.45
2a = 3.45 - 2.25
2a = 1.20
a = 1.20 / 2
a = 0.60
Therefore, the cost of one apple is $0.60, and the cost of one pear is $0.75.