Pepperidge Farm Goldfish is a snackfood for which 40% of its calories come from fat. Rold Gold Pretzels receive 9% of their calories from fat.How many grams of each would be needed to make 620g of a snack mix for which 15% of the calories come from fat?

let the amount of goldfish needed by x g

then the amount of pretzels needed is 620-x g

.4x + .09(620-x) = .15(620)
times 100
40x + 9(620-x) = 15(620)
40x - 5580 - 9x = 9300
31x = 14880
x = 480

Needed: 480 g of goldfish, and 140 g of pretzels

To determine the grams of Pepperidge Farm Goldfish and Rold Gold Pretzels needed to make a 620g snack mix with 15% fat calories, we can set up a system of equations.

Let x represent the grams of Pepperidge Farm Goldfish and y represent the grams of Rold Gold Pretzels needed.

1. Create an equation for the total grams of the snack mix:
x + y = 620 (Equation 1)

2. Create an equation for the fat calories in the snack mix:
0.40x + 0.09y = 0.15(620) (Equation 2)

Now we can solve the system.

Step 1: Solve Equation 1 for x:
x = 620 - y

Step 2: Substitute x in Equation 2 with the value obtained from Step 1:
0.40(620 - y) + 0.09y = 93

Step 3: Simplify the equation:
248 - 0.40y + 0.09y = 93
0.31y = 155
y = 155 / 0.31
y ≈ 500

Step 4: Substitute the value of y back into Equation 1 to solve for x:
x + 500 = 620
x = 620 - 500
x = 120

Therefore, you would need approximately 120g of Pepperidge Farm Goldfish and 500g of Rold Gold Pretzels to make a 620g snack mix where 15% of the calories come from fat.

To find out how many grams of Pepperidge Farm Goldfish and Rold Gold Pretzels are needed to make a 620g snack mix with 15% of calories from fat, we need to set up an equation.

Let's assume that the number of grams of Pepperidge Farm Goldfish is x, and the number of grams of Rold Gold Pretzels is y.

The total calories in the snack mix can be calculated as follows:
Total calories = Calories from Goldfish + Calories from Pretzels

Since 40% of calories come from fat in Goldfish and 9% in Pretzels, we can calculate the calories as:
Calories from Goldfish = 0.40 * x
Calories from Pretzels = 0.09 * y

The total calories in the snack mix would be:
Total calories = 0.15 * 620

To set up the equation, we equate the total calories to the calories from Goldfish and Pretzels:
0.15 * 620 = 0.40x + 0.09y

Now, we have one equation with two variables, so we need another equation to solve for the unknowns.
Since the total weight of the snack mix is 620g, we can set up another equation as:
Total weight = Weight of Goldfish + Weight of Pretzels
620 = x + y

Now, we have a system of two equations:
0.15 * 620 = 0.40x + 0.09y
620 = x + y

To solve the system of equations, we can use substitution or elimination. Let's use substitution:

Rearrange the second equation to solve for x:
x = 620 - y

Substitute this expression for x in the first equation:
0.15 * 620 = 0.40(620 - y) + 0.09y

Now, we can solve for y:

93 = 248 - 0.40y + 0.09y
0.49y = 155
y = 316.33

Substitute the value of y back into the second equation to solve for x:
620 = x + 316.33
x = 303.67

So, approximately 303.67 grams of Pepperidge Farm Goldfish and 316.33 grams of Rold Gold Pretzels would be needed to make a 620g snack mix with 15% of calories from fat.