Three friends are each making a fruit salad for a summer picnic. Zadie uses 6 pounds of strawberries, 10 pounds of grapes, and 2 pounds of melon, for a total cost of $30. Raquel uses 6 pounds of strawberries, 4 pounds of grapes, and 4 pounds of melon, for a total cost of $40. Joseph uses 8 pounds of strawberries, 6 pounds of grapes, and 5 pounds of melon, for a total cost of $55. Let s represent the pounds of strawberries, g represent the pounds of grapes, and m represent the pounds of melon in each salad. Create a system of three linear equations in three variables based on this description. Which of the following equations is part of the system?(1 point) Responses 6s+4g+2m=30 6 s plus 4 g plus 2 m equals 30 8s+6g+4m=55 8 s plus 6 g plus 4 m equals 55 6s+10g+2m=40 6 s plus 10 g plus 2 m equals 40 6s+4g+4m=40

Answer 1

To create a system of equations based on the fruit salad descriptions of Zadie, Raquel, and Joseph, we need to translate the information given into mathematical equations.

Let:

• \( s \) = cost per pound of strawberries
• \( g \) = cost per pound of grapes
• \( m \) = cost per pound of melon

From the information provided:

1. Zadie's fruit salad:

   • Uses 6 pounds of strawberries, 10 pounds of grapes, and 2 pounds of melon.
   • Total cost: $30.
   • The equation is: \[ 6s + 10g + 2m = 30 \]

2. Raquel's fruit salad:

   • Uses 6 pounds of strawberries, 4 pounds of grapes, and 4 pounds of melon.
   • Total cost: $40.
   • The equation is: \[ 6s + 4g + 4m = 40 \]

3. Joseph's fruit salad:

   • Uses 8 pounds of strawberries, 6 pounds of grapes, and 5 pounds of melon.
   • Total cost: $55.
   • The equation is: \[ 8s + 6g + 5m = 55 \]

So, the system of equations that we derived is:

1. \( 6s + 10g + 2m = 30 \)
2. \( 6s + 4g + 4m = 40 \)
3. \( 8s + 6g + 5m = 55 \)

From the options provided in the question, the equation that is part of this system is:

• 6s + 4g + 4m = 40

Thus, this means one of the correct equations from our derived set is \( 6s + 4g + 4m = 40 \).