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  1. Home
  2. 12th grade
  3. Algebra I
  4. Exercise : Convert a word problem into a system of linear equations

Convert a word problem into a system of linear equations Algebra I

Which system of linear equations is the best translation of the following word problems?

Let x be the price of an apple and y be the price of an orange. Paul buys 12 apples and 5 oranges for a total of $4.60. Marie buys 5 apples and 8 oranges for a total of $3.10.

We have:

  • x the number of apples
  • y the number of oranges

Paul buys 12 apples and 5 oranges, which is \left(12x+5y\right), and he pays $4.60. Therefore the first equation is:

12x+5y=4.6

Marie buys 5 apples and 8 oranges, which is \left(5x+8y\right), and she pays $3.10. Therefore the second equation is:

5x+8y=3.1

The problem can be solved by solving the following system:

\begin{cases} 12x+5y=4.6 \cr \cr 5x+8y=3.1 \end{cases}

Let x be the price of a gallon of gasoline and y be the price of a gallon of diesel fuel. Joe buys 5 gallons of gasoline and 15 gallons of diesel fuel for a total of $50.30. Lala buys 15 gallons of gasoline and 5 gallons of diesel for a total of $45.60.

We have:

  • x the number gallons of gasoline
  • y the number of gallons of diesel

Joe buys 5 gallons of gasoline and 15 gallons of diesel, which is \left(5x+15y\right), and he pays $50.30. Therefore the first equation is:

5x+15y=50.30

Lala buys 15 gallons of gasoline and 5 gallons of diesel, which is \left(15x+5y\right), and she pays $45.60. Therefore the second equation is:

15x+5y=45.60

The problem can be solved by solving the following system:

\begin{cases} 5x+15y=50.30 \cr \cr 15x+5y=45.60 \end{cases}

Let x be the price of one pound of beef and y be the price of one pound of chicken. Hisland buys 7 pounds of beef and 3 pounds of chicken for a total of $20. Ranny buys 18 pounds of beef and 12 pounds of chicken for a total of $35.

We have:

  • x the number of pounds of beef
  • y the number of pounds of chicken

Hisland buys 7 pounds of beef and 3 pounds of diesel, which is \left(7x+3y\right), and he pays $20. Therefore the first equation is:

7x+3y=20

Ranny buys 18 pounds of beef and 12 pounds of chicken, which is \left(18x+12y\right), and she pays $35. Therefore the second equation is:

18x+12y=35

The problem can be solved by solving the following system:

\begin{cases} 7x+3y=20 \cr \cr 18x+12y=35 \end{cases}

Let x be the price of one pound of horse feed and y be the price of one pound of chicken feed. Harvey buys 20 pounds of horse feed and 5 pounds of chicken feed for a total of $75. Dina buys 10 pounds of horse feed and 12 pounds of chicken feed for a total of $45.

We have:

  • x the number of pounds of horse feed
  • y the number of pounds of chicken feed

Harvey buys 20 pounds of horse feed and 5 pounds of chicken feed, which is \left(20x+5y\right), and he pays $75. Therefore the first equation is:

20x+5y=75

Dina buys 10 pounds of horse feed and 12 pounds of chicken feed, which is \left(10x+12y\right), and she pays $35. Therefore the second equation is:

10x+12y=45

The problem can be solved by solving the following system:

\begin{cases} 20x+5y=75 \cr \cr 10x+12y=45 \end{cases}

Let x be the price of a banana and y be the price of a kiwi fruit. Layla buys 8 bananas and 5 kiwi fruits for a total of $10.60. Apik buys 7 bananas and 12 kiwi fruits for a total of $12.50.

We have:

  • x the number of bananas
  • y the number of kiwi fruits

Layla buys 8 bananas and 5 kiwi fruits, which is \left(8x+5y\right), and he pays $10.60. Therefore the first equation is:

8x+5y=10.60

Apik buys 7 apples and 12 oranges, which is \left(7x+12y\right), and she pays $12.50. Therefore the second equation is:

7x+12y=12.50

The problem can be solved by solving the following system:

\begin{cases} 8x+5y=10.60 \cr \cr 7x+12y=12.50 \end{cases}

Let x be the price of a gallon of gasoline and y be the price of a gallon of diesel fuel. Josh buys 2 gallons of gasoline and 20 gallons of diesel fuel for a total $60. Tammy buys 20 gallons of gasoline and 0 gallons of diesel for a total of $50.

We have:

  • x the number gallons of gasoline
  • y the number of gallons of diesel

Josh buys 2 gallons of gasoline and 20 gallons of diesel, which is \left(2x+20y\right), and he pays $60. Therefore the first equation is:

2x+20y=60

Tammy buys 20 gallons of gasoline and 0 gallons of diesel, which is \left(20x+0y\right), and she pays $50. Therefore the second equation is:

20x+0y=50

The problem can be solved by solving the following system:

\begin{cases} 2x+20y=60 \cr \cr 20x=50 \end{cases}

Let x be the price of one pound of horse feed and y be the price of one pound of chicken feed. Drew buys 20 pounds of horse feed and 5 pounds of chicken feed for a total of $50. Dana buys 5 pounds of horse feed and 6 pounds of chicken feed for a total of $29.

We have:

  • x the number of pounds of horse feed
  • y the number of pounds of chicken feed

Drew buys 20 pounds of horse feed and 5 pounds of chicken feed, which is \left(20x+5y\right), and he pays $50. Therefore the first equation is:

20x+5y=50

Dana buys 5 pounds of horse feed and 6 pounds of chicken feed, which is \left(5x+6y\right), and she pays $29. Therefore the second equation is:

5x+6y=29

The problem can be solved by solving the following system:

\begin{cases} 20x+5y=50 \cr \cr 5x+6y=29 \end{cases}

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See also
  • Course : System of linear equations
  • Exercise : Solve a system of equation using substitution
  • Exercise : Solve a system of equation using elimination
  • Exercise : Convert a system of equations into a triangular system
  • Exercise : Solve a system of equation using the Gaussian elimination
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