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Consuelo is buying flavored coffee and plain coffee. The total amount of money she spends on coffee is T = 5.50p + 7f, where "p" represents the cost of a package of plain coffee and "f" represents the cost of a package of flavored coffee.
a. If Consuelo has $40 to spend on coffee, describe the constraints on the formula.
b. Solve for f.
c. If Consuelo needs to buy 3 packages of plain coffee, what is the maximum number of packages of flavored coffee she can buy?

Sagot :

MrRoyalidn

A linear equation can have one or more variables.

  • The constraints on the formula are the costs of plain coffee and cost of flavored coffee
  • The equation of f is: [tex]\mathbf{f = \frac{40 -5.50p}7 }[/tex].
  • The maximum number of packages of flavored coffee she can buy is 3

The function is given as:

[tex]\mathbf{T = 5.50p + 7f}[/tex]

(a) The constraints when T = 40

Substitute 40 for T in [tex]\mathbf{T = 5.50p + 7f}[/tex]

[tex]\mathbf{5.50p + 7f = 40}[/tex]

The variables in the above equation are p and f

Hence, the constraints are the cost of a package of plain coffee and the cost of a package of flavored coffee

(b) Solve for f

In (a), we have:

[tex]\mathbf{5.50p + 7f = 40}[/tex]

Subtract both sides by 5.50p

[tex]\mathbf{7f = 40 -5.50p }[/tex]

Divide both sides by 7

[tex]\mathbf{f = \frac{40 -5.50p}7 }[/tex]

Hence, the equation of f is:

[tex]\mathbf{f = \frac{40 -5.50p}7 }[/tex]

(c) The maximum number of flavored coffee when she buys 3 packages of plain coffee

In (b), we have:

[tex]\mathbf{f = \frac{40 -5.50p}7 }[/tex]

Substitute 3 for p

[tex]\mathbf{f = \frac{40 -5.50 \times 3}7 }[/tex]

[tex]\mathbf{f = \frac{40 -16.50}7 }[/tex]

[tex]\mathbf{f = \frac{23.5}7 }[/tex]

Divide

[tex]\mathbf{f = 3.36 }[/tex]

Remove the decimal part (do not approximate)

[tex]\mathbf{f = 3 }[/tex]

Hence, the maximum number of packages of flavored coffee she can buy is 3

Read more about linear equations at:

https://brainly.com/question/12420841

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