Six pears and three apples cost $3.90. Two pears and five apples cost $3.30. How much does one pear cost?
Hint: You have two unknowns (variables), so you need two equations. Write one equation for each situation and solve the system of equations.
(1): Six pears and three apples cost $3.90
(2): Two pears and five apples cost $3.30
(1) - 3*(2):
three apples - 15 apples cost $3.90 - 3*$3.30 --->
12 apples costs $6 -->
1 apple costs $0.50
And the pear costs $0.40 :)
To solve this problem, we can set up a system of equations using the information given. Let's represent the cost of one pear as "p" and the cost of one apple as "a".
From the first statement "Six pears and three apples cost $3.90", we can write the equation:
6p + 3a = 3.90
From the second statement "Two pears and five apples cost $3.30", we can write the equation:
2p + 5a = 3.30
To solve this system of equations, we can use the method of substitution or elimination. In this explanation, we will use the elimination method.
Multiply the first equation by 2 and the second equation by 6 to make the coefficients of "p" the same.
12p + 6a = 7.80
12p + 30a = 19.80
Now, subtract the second equation from the first equation:
(12p + 6a) - (12p + 30a) = 7.80 - 19.80
Simplifying the equation, we get:
-24a = -12
Divide both sides of the equation by -24:
a = -12 / -24
a = 0.50
Now, substitute the value of "a" back into either of the original equations. Let's use the first equation:
6p + 3(0.50) = 3.90
Simplifying the equation, we get:
6p + 1.50 = 3.90
Subtract 1.50 from both sides of the equation:
6p = 3.90 - 1.50
6p = 2.40
Divide both sides of the equation by 6:
p = 2.40 / 6
p = 0.40
Therefore, one pear costs $0.40.