Two apples and three pears cost $3.45. Three apples and five pears cost $5.55. Find the cost of each type of fruit.
Equations: Substitution
y = 2a + 3p = 345
y = 3a + 5p = 555
To solve this problem, we can set up a system of equations based on the given information.
Let's assume the cost of one apple is "a" dollars and the cost of one pear is "p" dollars.
From the first statement, we know that two apples and three pears cost $3.45, which can be written as:
2a + 3p = 3.45 (Equation 1)
From the second statement, we know that three apples and five pears cost $5.55, which can be written as:
3a + 5p = 5.55 (Equation 2)
Now, we need to solve this system of equations to find the values of "a" and "p".
There are several methods to solve this system, such as substitution or elimination. I will use the elimination method to demonstrate.
To eliminate one variable, we can multiply Equation 1 by 3 and Equation 2 by 2. This gives us:
6a + 9p = 10.35 (Equation 3)
6a + 10p = 11.1 (Equation 4)
Now, let's subtract Equation 3 from Equation 4 to eliminate "a":
(6a + 10p) - (6a + 9p) = 11.1 - 10.35
This simplifies to:
p = 0.75
Now, we have the value of "p" (the cost of one pear). We can substitute this value back into one of the original equations to find the value of "a".
Let's substitute "p = 0.75" into Equation 1:
2a + 3(0.75) = 3.45
2a + 2.25 = 3.45
Subtracting 2.25 from both sides, we have:
2a = 1.20
Dividing both sides by 2, we find:
a = 0.60
So, the cost of one apple is $0.60 and the cost of one pear is $0.75.