Math CentralQuandaries & Queries


Question from Karen, a student:

Mr. Pace bought breakfast for his first period class. Ten donuts and fifteen bagels
cost a total of $15.75. Mrs. Pace bought breakfast for her class. Five donuts and twenty
bagels cost a total of $17.00. Set up and solve a system of linear equations to determine the cost
of one donut and one bagel.

So far, this is what I've come up with. Please add corrections and additional information to my work.
Also, please show me how to solve.

x=cost for each donut
y=cost for each bagel

Mr. Pace: 10x+15y=15.75
Mrs.Pace: 5x+20y=17.00

What steps do you do next? Thanks.

Hi Karen,

I agree with your two equations

Mr. Pace: 10x+15y=15.75
Mrs.Pace: 5x+20y=17.00

One thing I see in the two equations is that Mr. Pace bought twice as many donuts as Mrs. Pace. If we double Mrs. Pace's order so that they both buy the same number of donuts then the orders would be

Mr. Pace: 10x+15y=15.75
Mrs.Pace: 10x+40y=34.00

So in this case Mrs. Pace made the same order as Mr. Pace and then ordered 25 more bagels and paid an extra $34.00 - $15.75 = $18.25. Thus 25 bagels cost $18.25 so how much does one bagel cost?

Let's do that again but say it slightly differently. The equations are


Multiply the second equation by 2 to get


Subtract equation 1 from equation 2 and get

25 y = $18.25

Solve for y.

I hope this helps,

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