Question

The function for the cost of materials to make a muffin is f(x) = Three fourths x + 3, where x is the number of muffins. The function for the selling price of those muffins is g(f(x)), where g(x) = 3x + 4. Find the selling price of 20 muffins.

18
49
51
58

Answer 1

I made a mistake since it is g of fx then you will need to put the fx equation into the g equation as the x and then solve for x.

Answer 2

sooo....

g(3/4 *18 + 3) = 3(3/4*18+3) + 4

Answer 3

@ganeshie8 @hartnn

Answer 4

Correct! I would simplify and then plug in the 20! You're good on simplifying?

Answer 5

i have no idea how to do this part now... .-.

Answer 6

Your f(x) is,

\(\color{#000000 }{ \displaystyle f(x)=\frac{3}{4}(x+3) }\)

or is it,

\(\color{#000000 }{ \displaystyle f(x)=\frac{3}{4}x+3 }\)

Answer 7

no parenthesis :) so first.

Answer 8

i mean second lmao

Answer 9

The selling price any "x" muffins is modeled as

\(\color{#000000 }{ \displaystyle g(f(x))=4(f(x))+4=4(\frac{3}{4}x+3)+3 }\) ($ of selling muffins)

So, selling price of 20 muffins would be

\(\color{#000000 }{ \displaystyle g(f(\color{red}{20}))=3(\frac{3}{4}\cdot \color{red}{20}+3)+4=~.... }\)

Answer 10

idk how to simplify ;( @SolomonZelman

Answer 11

is it 58 ?

Answer 12

I would simplify at this point,

\(\color{#000000 }{ \displaystyle g(f(x))=4(f(x))+4 =4(\frac{3}{4}x+3)+3\\[1.3em] \displaystyle {\small \rm (here)\quad \quad } =(3x+12)+3=3x+15 }\)

Answer 13

you shoud be able to tell that for even x, you get even+odd=odd, so 58 is incorrect.

Answer 14

oh, sorry

Answer 15

I would simplify at this point,

\(\color{#000000 }{ \displaystyle g(f(x))=4(f(x))+4 =4(\frac{3}{4}x+3)+4\\[1.3em] \displaystyle {\small \rm (here)\quad \quad } =(3x+12)+4=3x+16 }\)

Answer 16

but, 58 is still not correct

Answer 17

(although it would actually be even)

Answer 18

3•20+16 =?

Answer 19

76

Answer 20

@SolomonZelman