Question

Alan, Beti and Cecil were the only people who baked cookies for a bake sale. Alan baked 32 cookies fewer than one-half of the cookies. Beti baked 24 cookies fewer than one- third of the cookies. Cecil baked 8 cookies more than one-quarter of the cookies. How many cookies were baked in total

Answer 1

Let's set up four equations. \[\text{Alan:} ~ A = 0.5 x - 32\]\[\text{Beti:}~ B = 0.3 x - 24\]\[\text{Cecil:}~ C = 0.25x + 8\]\[A + B + C = x\]

Answer 2

why is it 0.3x? should is be 0.33333333333333, since it is one-third?

Answer 3

You are right, but for this problem we don't need nearly that many decimal places.

Answer 4

oh, ok

Answer 5

Do you know how to solve those four equations for x?

Answer 6

yeah, sort of
what do i do now 1.05x-48=x

Answer 7

Solve for x by itself. \[x = {48 \over 0.05}\]

Answer 8

With a decimal that small, the lack of decimals in the 1/3 will cause a problem. Let's solve it using fractions.

\[{1 \over 2} + {1 \over 4} + {1 \over 3} = {6 \over 12} + {3 \over 12} + {4 \over 12} = {13 \over 12}\]\[x = 48 * {12}\]

Answer 9

thx