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 = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (2, 14) and (x₂, y₂ ) = (3, 18.5) ← 2 ordered pairs from the table
m = [tex]\frac{18.5-14}{3-2}[/tex] = [tex]\frac{4.5}{1}[/tex] = 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 = [tex]\frac{27-23}{3-2}[/tex] = [tex]\frac{4}{1}[/tex] = 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
