Four pears and two apples cost $1.96. Three apples and three pears cost $2.10. Find the cost of 1 apple and 1 pear.
4p + 2a = 196
3p + 3a = 210
divide the second equation by 3, solve for p, then sub that into the first.
To find the cost of 1 apple and 1 pear, let's assign variables to the unknowns. Let's say the cost of 1 apple is 'a' dollars and the cost of 1 pear is 'p' dollars.
From the given information, we can set up two equations:
Equation 1: 4p + 2a = 1.96 (Four pears and two apples cost $1.96)
Equation 2: 3p + 3a = 2.10 (Three apples and three pears cost $2.10)
To solve the system of equations, we can use the method of substitution or elimination. In this case, let's use the method of substitution.
Step 1: Solve Equation 1 for 'a':
2a = 1.96 - 4p
a = (1.96 - 4p) / 2
a = 0.98 - 2p
Step 2: Substitute the value of 'a' in Equation 2:
3p + 3(0.98 - 2p) = 2.10
3p + 2.94 - 6p = 2.10
-3p = 2.10 - 2.94
-3p = -0.84
p = (-0.84) / -3
p = 0.28
Step 3: Substitute the value of 'p' back into Equation 1 to find 'a':
a = 0.98 - 2(0.28)
a = 0.98 - 0.56
a = 0.42
Therefore, the cost of 1 apple is $0.42 and the cost of 1 pear is $0.28.