Question

To prepare for soccer season, Hanzel wants to eat 40 grams ofprotein at breakfast. He knows that there are 2 grams ofprotein in a slice of bacon and 4 grams of protein in an egg.Let b represent the number of slices of bacon he will eat, andlet g represent the number of eggs he will eat.a) Write an equation that relates the number of slices of baconto the number eggs he will eat, assuming he eats exactly 40grams of protein.b) List some possible solutions.slices of bacon, 1 egg8 slices of bacon,eggsslices of bacon, 3 eggsc) Rewrite your equation in slope-intercept form.no

Answer 1

Let's begin by identifying key information given to us:

Hanzel wants to eat 40 grams of protein at breakfast: Aim = 40 grams

A slice of bacon = 2 grams

An egg = 4 grams

Let b represent the number of slices of bacon he will eat

Let g represent the number of eggs he will eat

a)

We have our equation thus:

slice of bacon + eggs = 40

Assuming he eats exactly 40 grams of protein, the equation is:

`2b+4g=40`

b)

Possible solutions we can have:

`\begin{gathered} 2b+4g=40 \\ b=8,e=6 \\ 2(8)+4(6)=16+24=40 \\ 8SlicesOfBacon;6Eggs \\ b=12,e=4 \\ 2(12)+4(4)=24+16=40 \\ 12SlicesOfBacon;4Eggs \\ b=16,e=2 \\ 2(16)+4(2)=32+8=40 \\ 16SlicesOfBacon;2Eggs \end{gathered}`

c)

Rewrite your equation in slope-intercept form means we will write the equation in the form y = mx + b

`\begin{gathered} 2b+4g=40 \\ \text{Subtract 2b from both sides (assuming g is dependent var.), we have:} \\ 2b-2b+4g=-2b+40 \\ 4g=-2b+40 \\ \text{Divide through every element by 4, we have:} \\ (4g)/(4)=-(2b)/(4)+(40)/(4)\Rightarrow g=-(1)/(2)b+40 \\ g=-(1)/(2)b+40 \end{gathered}`