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)

Question

Responses

6s+4g+2m=30
6
𝑠
+
4
𝑔
+
2
𝑚
=
30
6 s plus 4 g plus 2 m equals 30

6s+10g+2m=40
6
𝑠
+
10
𝑔
+
2
𝑚
=
40
6 s plus 10 g plus 2 m equals 40

6s+4g+4m=40
6
𝑠
+
4
𝑔
+
4
𝑚
=
40
6 s plus 4 g plus 4 m equals 40

8s+6g+4m=55

Answer 1

To create a system of three linear equations based on the description of the fruit salads made by Zadie, Raquel, and Joseph, we can translate the information given into equations where \( s \) represents the cost of strawberries per pound, \( g \) represents the cost of grapes per pound, and \( m \) represents the cost of melon per pound.

1. Zadie's salad:

   • 6 pounds of strawberries, 10 pounds of grapes, and 2 pounds of melon for a total cost of $30: \[ 6s + 10g + 2m = 30 \]

2. Raquel's salad:

   • 6 pounds of strawberries, 4 pounds of grapes, and 4 pounds of melon for a total cost of $40: \[ 6s + 4g + 4m = 40 \]

3. Joseph's salad:

   • 8 pounds of strawberries, 6 pounds of grapes, and 5 pounds of melon for a total cost of $55: \[ 8s + 6g + 5m = 55 \]

Now, we put together the equations we've formed:

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

Among the given options, the following equation is part of the system:

6s + 4g + 4m = 40

So the correct response is: 6s + 4g + 4m = 40