Question

Help me with this I will give brainliest

Answer 1

Answer:

see explanation

Step-by-step explanation:

both linear equations will have the form

y = mx + c ( m is the slope and c the y- intercept )

Chef Mate

c(n) = mn + c

calculate m using the slope formula

m = $\frac{y_{2}-y_{1} }{x_{2}-x_{1} }$

with (x₁, y₁ ) = (2, 14) and (x₂, y₂ ) = (3, 18.5) ← 2 ordered pairs from the table

m = $\frac{18.5-14}{3-2}$ = $\frac{4.5}{1}$ = 4.5 , then

c(n) = 4.5n + c ( n represents ounces )

To find c substitute any ordered pair from the table into c(n)

using (4, 23 )

23 = 18 + c ⇒ c = 23 - 18 = 5

c(n) = 4.5n + 5 ← equation for Chef Mate

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Similarly for Grocery Gourmet

g(n) = mn + c

using (2, 23 ) and (3, 27 ) to find m

m = $\frac{27-23}{3-2}$ = $\frac{4}{1}$ = 4 , then

g(n) = 4n + c

using (4, 31 ) to find c

31 = 16 + c ⇒ c = 31 - 16 = 15

g(n) = 4n + 15 ← equation for Grocery Gourmet

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Equate the 2 equations to find when cost is the same

4.5n + 5 = 4n + 15 ( subtract 4n from both sides )

0.5n + 5 = 15 ( subtract 5 from both sides )

0.5n = 10 ( divide both sides by 0.5 )

n = 20

Then when n = 20

c(n) = 4.5(20) + 5 = 90 + 5 = 95

g(n) = 4(20) + 15 = 80 + 15 = 95

Both Chef Mate and Grocery Gourmet charge $95 for 20 ounces of extract