Question

You are in charge of bringing breakfast for your scout troop. You buy 6 bagels and 8 donuts for a total of \(4.10. Then you decide to buy 3 extra of each for a total of \)1.80. How much did each bagel and donut cost?

Short answer

Each bagel costs $0.35 and each donut costs $0.25.

Step-by-step solution

Represent the problem with equations

Let's denote the cost of a bagel as \(b\) and the cost of a donut as \(d\). According to the problem statement, we can form these two equations: 6b + 8d = 4.10 (equation 1 presenting the first purchase) and 3b + 3d = 1.80 (equation 2 presenting the second purchase).

Modify the equations to solve for the variables

Multiply equation 2 by 2: 6b + 6d = 3.60. Now, we have two equations with the same coefficient for \(b\): 6b + 8d = 4.10 and 6b + 6d = 3.60.

Subtract one equation from the other

Subtract the second equation from the first one to isolate \(d\): 2d = 0.50. Divide each side by 2 to get the value for \(d\): \(d\) = 0.25.

Substitute the value of d into one of the equations

Now, plug \(d = 0.25\) into equation 2: 3b + 3*0.25 = 1.80. Therefore, 3b + 0.75 = 1.80. Subtract 0.75 from both sides: 3b = 1.05. Divide by 3 to solve for \(b\): \(b\) = 0.35.