Meaghan goes to the grocery store to buy hot dogs and hamburgers for a cookout. She buys a total of 12
packages for a total of $36.88. If a package of hot dogs, d, costs $2.59 and a package of hamburgers, b,
costs $5.49, determine how many packages of each she bought.
Enter a system of equations to represent the situation, then solve the system.
The system of equations is_and_
Meaghan bought _
packages of hot dogs and____
packages of hamburgers.

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absor201 absor201 · Answer 1 · 2019-12-19T17:54:37+01:00

The system of equations is d+b=12 and 2.59d+5.49b=36.88 and Meaghan bought 10 packages of hot dogs and 2 packages of hamburgers.

Step-by-step explanation:

Cost of one package of hot dog = $2.59

Cost of one package of hamburgers = $5.49

Packages bought = 12

Cost of packages = $36.88

Let,

Packages of hot dogs = d

Packages of hamburger = b

According to given statement;

d+b=12 Eqn 1

2.59d+5.49b=36.88 Eqn 2

Multiplying Eqn 1 by 2.59

[tex]2.59(d+b=12)\\2.59d+2.59b=31.08\ \ \ Eqn\ 3[/tex]

Subtracting Eqn 3 from Eqn 2

[tex](2.59d+5.49b)-(2.59d+2.59b)=36.88-31.08\\2.59d+5.49b-2.59d-2.59b=5.80\\2.90b=5.80[/tex]

Dividing both sides by 2.90

[tex]\frac{2.90b}{2.90}=\frac{5.80}{2.90}\\b=2[/tex]

Putting b=2 in Eqn 1

[tex]d+2=12\\d=12-2\\d=10[/tex]

The system of equations is d+b=12 and 2.59d+5.49b=36.88 and Meaghan bought 10 packages of hot dogs and 2 packages of hamburgers.

Keywords: linear equation, elimination method

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