A school cafeteria sells sandwiches for $4.50 each, cartons of milk for $1 and bananas for $.50 each. One table of students spent $36.00 total. They bought 2 more milks than sandwiches and they bought two times more sandwiches than bananas. How many bananas did the students buy?
I don't understand (obviously) 3 bananas ends up at $36.50, 2 ends up at $25.00 and 2 and 1/2 ends up at $30.75. This is my sons 6th grade homework and I really doubt they are looking for an answer of 2.85 bananas so what am I doing wrong here?
number of bananas ---- x
sandwiches -----------2x
milks ---------- 2x + 2
.5x + 4.5(2x) + 1(2x+2) = 36
.5x + 9x + 2x + 2 = 36
11.5x = 34
x = 2.9 ..... ah!!
No wonder you can't make sense of the problem, the data is flawed.
If the question appears that way in the text, there must be a typo, since x clearly must turn out to be a whole number.
To find the number of bananas the students bought, let's break down the information given and analyze it step by step.
Let's assume the number of sandwiches the students bought is 'x.'
Given that they bought two times more sandwiches than bananas, we can represent the number of bananas as 'x/2'.
Also, they bought two more milks than sandwiches, so the number of milks can be expressed as 'x + 2'.
Now, let's calculate the total cost of their purchases:
The cost of the sandwiches is $4.50 each, so the total cost of sandwiches is 4.50 * x.
The cost of the milks is $1 each, so the total cost of milks is 1 * (x + 2).
The cost of the bananas is $0.50 each, so the total cost of bananas is 0.50 * (x/2).
The total cost of all their purchases is $36.
Therefore, we can write the equation:
4.50 * x + 1 * (x + 2) + 0.50 * (x/2) = 36.
Simplifying the equation:
4.50x + x + 2 + 0.50(x/2) = 36.
Combine like terms:
4.50x + x + 2 + 0.25x = 36.
5.75x + 2 = 36.
5.75x = 34.
Dividing both sides by 5.75:
x = 34 / 5.75.
x ≈ 5.91.
Since we can't have a fraction of a sandwich, we need to round down to the nearest whole number. Therefore, x = 5.
Now, let's calculate the number of bananas:
The number of bananas is x/2 = 5/2 = 2.5.
Again, we need to round down to the nearest whole number since we can't buy a fraction of a banana. Therefore, the students bought 2 bananas.
So, the answer to your question is that the students bought 2 bananas.
However, it seems there might be an error in the given information or assumption, as the calculations above suggest. It's always good to double-check the problem statement and calculations to ensure accuracy.