a cup of coffee cost .75 cents more than a donut, angelo buys 6 donuts and 2 muffins which cost 12.50 total. how much does 1 muffin cost
Let's say the cost of a donut is x.
Therefore, the cost of a cup of coffee is x + $0.75.
The cost of 6 donuts is 6x.
The cost of 2 muffins is 2 * cost per muffin = $2x.
The total cost of 6 donuts and 2 muffins is 12.50, so 6x + 2x = 12.50.
Combining like terms, we get 8x = 12.50.
Dividing both sides by 8, we get x = 12.50 / 8 = $1.5625.
Therefore, the cost of one muffin is $2x = $2 * $1.5625 = $3.125. Answer: \boxed{3.125}.
To find the cost of one muffin, we can set up a system of equations based on the given information. Let's define the variables:
Let x be the cost of one donut.
Given that a cup of coffee costs $0.75 more than a donut, we can define the cost of a cup of coffee as x + $0.75.
Now, let's create an equation based on the total cost of Angelo's purchase:
6 donuts * x + 2 muffins * (cost of one muffin) + 2 muffins * (cost of one coffee) = $12.50
Since Angelo buys 2 muffins, the total cost of muffins is 2 * (cost of one muffin), and the total cost of coffee is 2 * (cost of one coffee).
Substituting the previously defined values into the equation, we get:
6x + 2(cost of one muffin) + 2(x + $0.75) = $12.50
Now, we can simplify the equation:
6x + 2(cost of one muffin) + 2x + 1.50 = $12.50
Combining like terms:
8x + 2(cost of one muffin) + 1.50 = $12.50
Now, let's isolate the variable:
8x + 2(cost of one muffin) = $12.50 - $1.50
8x + 2(cost of one muffin) = $11.00
Subtracting 2(cost of one muffin) from both sides of the equation:
8x = $11.00 - 2(cost of one muffin)
Since we want to find the cost of one muffin, we'll express it on one side of the equation:
2(cost of one muffin) = $11.00 - 8x
Now, divide both sides of the equation by 2 to solve for the cost of one muffin:
(cost of one muffin) = ($11.00 - 8x) / 2
So, the cost of one muffin is ($11.00 - 8x) / 2.
Let's set up a system of equations to solve this problem:
Let D be the cost of one donut.
Then the cost of one cup of coffee would be D + 0.75 cents.
According to the given information:
6 donuts would cost 6D.
2 muffins would cost 2M.
And the total cost of 6 donuts and 2 muffins is $12.50.
So, we have the equation: 6D + 2M = 12.50.
Now let's solve for the cost of one muffin, M:
From the first equation, we know that the cost of one cup of coffee is D + $0.75.
Since Angelo did not buy any coffee, the cost of the coffee is zero.
So, the equation becomes: 6D + 2M + 0 = 12.50.
Simplifying the equation: 6D + 2M = 12.50.
Now we have a system of two equations:
6D + 2M = 12.50, and
D + 0.75 = 0.
From the second equation, we can determine the value of D:
D = -0.75.
Substituting this value into the first equation:
6(-0.75) + 2M = 12.50.
Simplifying the equation: -4.50 + 2M = 12.50.
Next, isolate the variable M by subtracting -4.50 from both sides:
2M = 12.50 + 4.50.
Simplifying the equation: 2M = 17.
Finally, divide both sides by 2 to solve for M:
M = 17 / 2.
Therefore, one muffin costs $8.50.