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}