Andrew’s fruit shop had a total of 295 apples and pears. He sold 1/3 of the pears and bought another 50 apples. in the end, there was an equal number of apples and pears in the shop. How many more pears than apples were there in the shop at first.
at the start:
number of apples --- x
number of pears ---- 295-x
after transaction he has:
number of apples = 2x/3
number of pears = 295-x + 50 = 345 - x
they are the same, so ...
2x/3 = 345 - x
5x/3 = 345
x = 207
so at the start he had 207 apples, and 88 pears.
State your conclusion
Incorrect answer. Respond back
It’s correct
Actually I read it as:
He sold 1/3 of the apples and bought another 50 pears, so I had
the fruits backwards.
I think it would be a great learning experience if you corrected my
post. Let me know what the correct answer is that you got.
It was 119 but your corrct
To solve this problem, let's break it down step by step:
Step 1: Determine the number of apples and pears Andrew had originally.
Let's assume the number of apples Andrew had originally was "A," and the number of pears he had originally was "P." We know that the total number of apples and pears is 295, so we can form an equation: A + P = 295.
Step 2: Find the number of pears Andrew sold and bought.
We are told that Andrew sold 1/3 of the pears, which means he had P - (1/3)P pears remaining. Then, he bought 50 more apples, so the new number of apples became A + 50.
Step 3: Set up the final equation based on the given information.
We know that in the end, the number of apples and pears was the same. Therefore, we can form another equation: A + 50 = P - (1/3)P.
Step 4: Solve the equations to find the values of A and P.
Now, we have a system of two equations with two unknowns:
A + P = 295 (equation from Step 1)
A + 50 = P - (1/3)P (equation from Step 3)
To solve this system of equations, we can substitute the value of A from equation 1 into equation 2:
(295 - P) + 50 = P - (1/3)P
Simplifying the equation:
345 - P = (2/3)P
Adding P to both sides:
345 = (2/3)P + P
Combining like terms:
345 = (5/3)P
Now, we can solve for P by multiplying both sides by 3/5:
P = (3/5) * 345
P = 207
Step 5: Calculate the number of apples originally.
Using equation 1, we can substitute the value of P to find A:
A + 207 = 295
A = 295 - 207
A = 88
Step 6: Determine the difference between the number of pears and apples originally.
The number of pears originally is P = 207, and the number of apples originally is A = 88. To find the difference, subtract the number of apples from the number of pears:
Difference = P - A
Difference = 207 - 88
Difference = 119
Therefore, initially, there were 119 more pears than apples in Andrew's fruit shop.