simultanious equations

[Bec]

Hi Guys, stuck on this question: It costs $9.80 to buy 5 plain doughnuts and 5 iced doughnuts. Given that each iced
doughnut costs 50% more than a plain doughnut, find the individual costs of a plain
doughnut and an iced doughnut.. if someone could help me out without what the two equations should be I should be right from there. Thanks

 

[Deleted member 4993]

Hi Guys, stuck on this question: It costs $9.80 to buy 5 plain doughnuts and 5 iced doughnuts. Given that each iced
doughnut costs 50% more than a plain doughnut, find the individual costs of a plain
doughnut and an iced doughnut.. if someone could help me out without what the two equations should be I should be right from there. Thanks

However, in these problems - 80% of the credit is for writing out the correct equations.

So I'll do a similar but different problem for you so that you can follow it and solve your problem.

It costs $15 to buy 10 plain doughnuts and 12 filled doughnuts. Given that each filled
doughnut costs 25% more than a plain doughnut, find the individual costs of a plain
doughnut and a filled doughnut.

Let

the cost of one plain-doughnut = P

the cost of one filled-doughnut = F

each filled doughnut costs 25% more than a plain doughnut → F = 1.25 * P .................. (1)

It costs $15 to buy 10 plain doughnuts and 12 filled doughnuts → 10 * P + 12*F = 15 ......(2)

Using (1) in (2)

10*P + 12*1.25*P = 15

10*P + 15*P = 15

P = 15/25 = 0.6 ....................................(3) ......... Answer

using (3) in (1)

F = 1.25 * 0.6 = 0.75.............................(4) ......... Answer

Now do your problem....