Mickey is very picky and insists that his mom makes his breakfast with equal parts of cereal and apple juice.
Any other combination ends up on the floor. Cereal costs 4 cents per tablespoon and apple juice costs 6 cents
per tablespoon. If his mom budgets $8 per month for his breakfast, how much cereal and juice does she buy?
The answer is 80 spoons of each.
To find out how much cereal and apple juice Mickey's mom buys, we need to set up an equation based on the given information. Let's assume the number of tablespoons of cereal Mickey's mom buys is represented by 'c', and the number of tablespoons of apple juice is represented by 'a'.
According to the problem, Mickey's mom mixes equal parts of cereal and apple juice. So, the cost of the cereal will be equal to the cost of the apple juice. We can set up the equation as follows:
4c = 6a
We also know that Mickey's mom has a budget of $8 per month for his breakfast. The total cost of the cereal and apple juice should not exceed $8. So, we can set up another equation using the costs per tablespoon:
4c + 6a ≤ 8
Now we have a system of equations to solve simultaneously:
1) 4c = 6a
2) 4c + 6a ≤ 8
To solve this system, we can substitute the value of c from the first equation into the second equation:
4c + 6a ≤ 8
4(6a/4) + 6a ≤ 8
6a + 6a ≤ 8
12a ≤ 8
Dividing both sides by 12:
a ≤ 8/12
a ≤ 2/3
This means, the maximum value of a can be 2/3.
Now we can substitute this value back into the first equation to find the value of c:
4c = 6(2/3)
4c = 4
c = 4/4
c = 1
So, Mickey's mom buys 1 tablespoon of cereal and 2/3 tablespoons of apple juice to stay within her budget.
To find out how much cereal and juice Mickey's mom buys, we can set up a system of equations based on the given information.
Let's assume Mickey's mom buys x tablespoons of cereal and y tablespoons of apple juice.
According to the problem, Mickey insists on having equal parts of cereal and apple juice, so we can set up the following equation:
x = y
Now, let's calculate the cost of the cereal and apple juice:
Cost of cereal = 4 cents per tablespoon * x tablespoons
Cost of apple juice = 6 cents per tablespoon * y tablespoons
The total cost should be within the budget of $8 per month, so we can set up another equation:
4x + 6y = 800 (since 1 dollar = 100 cents)
Now, we have a system of equations:
x = y
4x + 6y = 800
To solve this system, we can use substitution:
Substituting the value of x from the first equation into the second equation, we get:
4(y) + 6y = 800
4y + 6y = 800
10y = 800
y = 800 / 10
y = 80
Since x = y, we can conclude that x = 80 as well.
Therefore, Mickey's mom buys 80 tablespoons of cereal and 80 tablespoons of apple juice.