I am horrible with word problems I need help.

Question

The Smiths are expecting a total of 24 guests 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 the guests is $92.30. A dozen hot cross buns costs 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 box of Peeps.

Answer 1

Let X = cost of a box of peeps 

 

Then 12 hot cross buns cost X + 56

 

A pound of ham costs 2*(X + (X+56)) = 2*(2*X + 56) = 4*X + 112 

 

Each guest got a box of peeps, 3 hot cross buns and 1/3 pound of ham, so the cost for each guest was 

 

X + (X+56)/4 + (4*X + 112)/3 

 

There were 24 guests, so the total cost was 24 times this amount 

 

24*X + 6*(X+56) + 8*(4*X+112) 

 

Total cost was $92.30 so 

 

24*X + 6*X + 336 + 32*X + 896 = 9230

62*X + 1232 = 9230

62*X = 7998

 

X = 129 = $1.29 was the cost of a box of peeps 

 

Check:  Cost of 12 hot cross buns was $1.29 + 0.56 = $1.85

            Cost of a pound of ham was 2($1.29 + $1.85) = $6.28 

            24 guests received 24 boxes of peeps, 24*3 = 72 hot cross buns, and 24/3 = 8 pounds of ham, so total cost was

 

            24*1.29 + 6*1.85 + 8*6.28 = 30.96 + 11.10 + 50.24 = $92.30 

Answer 2

Let assume

The cost of box of peep =x

 

The cost of  dozen hot cross buns=x+56

 

so cost of  1 hot cross bun=(x+56)/12

 

The cost of a pound of ham =2(x +(x+56))=2(2x+56)=4x+112

 

 

Equations

Each guest will get a box of peeps, 3 hot cross buns, and 1/3 of a pound of ham

 

a box of peeps=x

3 hot cross buns=3(x+56)/12=(x+56)/4

1/3 of a pound of ham=1/3(4x+112)=(4x+112)/3

 

 

The total cost of the Peeps, buns, and ham for all the guests is $92.30

 

$92.30=9230 cents

total cost is for 24 guest so

 

24(x  + (x+56)/4  +(4x+112)/3=9230

 

After simplifying

 

x=129 cents

 

x= $ 1.29 cents

 

The cost of box of peep=$ 1.29