Question

The Smiths are expecting a total of 24 guest for Easter dinner. each guest will get a box of peeps 3 hot cross buns and 1/3 of a pound of ham. the total cost of the peeps, buns, and ham for all guests is $92.30. A dozen hot cross buns cost 56 cents more than a box of peeps and a pound of ham costs twice as much as the combined cost of a box of peeps and a dozen hot cross buns. find the cost of a box of peeps.

Answer 1

so hmmm we know 24 folks are coming over, and each are getting 1 box of peeps, 3 hot buns, and 1/3lb of ham
alrite, how much is that for 24 folks?

well, 24 boxes of peeps, 72 hotbuns and 8lbs of ham, we know the total for all those is 92.30 or 9230 in cents

let's say
p = price of peeps
b = price of hotbuns
h = price of lb of ham

so, thus then 24p + 72b + 8h = 9230

now, we know 12 "b" is 56 cents more than "p"
thus  12b = p + 56

we also know, a pound of ham is twice as "p + 12b" or h = 2(p + 12b)

thus  $\bf 24p+72b+8h=9230\quad \begin{cases} \underline{12b}=p+56\implies \boxed{b}=\cfrac{p+56}{12}\\\\ h=2(p+\underline{12b})\implies h=[2(p+p+56)]\\\\ \qquad h=2(2p+56)\implies h=4p+112 \end{cases}\\\\ -----------------------------\\\\ 24p+72\left( \boxed{\cfrac{p+56}{12} }\right)+8(4p+112)=9230$

solve for "p"