Michel wants to buy his mother handmade chocolates for Mother’s Day. He has $15.00 to spend. The price of each type of chocolate is given below.

Question

Fudge centres: $0.60 Nut clusters: $0.75 Truffles: $0.80

C. Michel’s final choice costs $14.80. It is a combination of all three types of chocolates.
a) Determine four possible combinations of chocolates he
could have selected.
b) Create and evaluate an algebraic expression to show that
each of your combinations works.

Answer 1

number of Fudge centres --- f
Nut clusters ----- n
Truffles -----t , where f, n, and t are whole numbers

.60f + .75n + .80t = 14.80
times 100
60f + 75n + 80t = 1480
divide by 5
12f + 15n + 16t = 296 <----- my algebraic expression
f = (296 - 15n - 16t)/12
you know that f must be a multiple of 12
and n < 19 , t < 18 , also n has to be even for (296-15n-16t) to stay even.

start guessing:
let n = 2 , t = 1, f = (296-30-16)/12 = 20.8 , not possible
let n = 4, t = 5, f = (296 - 60 - 80)/12 = 13
yeah, we got one!

check:
13(.60) + 4(.75) + 5(.80) = 14.80 , that's nice!

with the above restrictions in mind, "guess" at some other
values of n, t, and f

Answer 2

The line near the middle of the solution saying
"you know that f must be a multiple of 12"

should have said:
you know (296 - 15n - 16t) must be a multiple of 12