Question

Meaghan goes to the grocery store to buy hot dogs and hamburgers for a cookout. She buys a total of 12

Answer 1

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

$2.59(d+b=12)\\2.59d+2.59b=31.08\ \ \ Eqn\ 3$

Subtracting Eqn 3 from Eqn 2

$(2.59d+5.49b)-(2.59d+2.59b)=36.88-31.08\\2.59d+5.49b-2.59d-2.59b=5.80\\2.90b=5.80$

Dividing both sides by 2.90

$\frac{2.90b}{2.90}=\frac{5.80}{2.90}\\b=2$

Putting b=2 in Eqn 1

$d+2=12\\d=12-2\\d=10$

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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