Final answer:
Setting up a system of equations and using the elimination method reveals the cost of one donut is $0.80 and one cup of coffee is $1.25. Therefore, the cost for 2 donuts and 1 cup of coffee totals $2.85.
Step-by-step explanation:
The question posed is trying to determine the combined cost of two donuts and one cup of coffee based on provided total costs for larger quantities of these items purchased for police officers and detectives. We can set up a system of equations to solve for the price of a single donut and a single cup of coffee. Let d be the cost of one donut and c be the cost of one cup of coffee.
For the police officers: 18d + 12c = $29.40
For the detectives: 12d + 10c = $22.10
To solve for d and c, we can use the method of substitution or elimination. Let's use elimination:
- Multiply the entire second equation by 1.5, which gives:
18d + 15c = $33.15 - Now, subtract the first equation from this new equation:
(18d + 15c) - (18d + 12c) = ($33.15 - $29.40), which simplifies to
3c = $3.75. - Divide both sides by 3 to find the cost of one cup of coffee: c = $1.25.
- Now, we can substitute c = $1.25 into one of the original equations to find d.
- Substituting into the first equation: 18d + 12($1.25) = $29.40. This simplifies to 18d + $15 = $29.40.
- Subtract $15 from both sides: 18d = $14.40.
- Divide by 18: d = $0.80.
- Now we can find the cost of 2 donuts and 1 cup of coffee: 2d + c = 2($0.80) + $1.25 = $1.60 + $1.25 = $2.85.
Therefore, the cost for 2 donuts and 1 cup of coffee is $2.85.