Question

A store is having a sale on jelly beans and trail mix. For 8 pounds of jelly beans and 4 pounds of trail mix, the total cost is $37. For 3 pounds of jelly beans and 2 pounds of trail mix, the total cost is $15. Find the cost for each pound of jelly beans and each pound of trail mix.

Answer 1

Let x be the cost per pound of jelly beans and y be the cost per pound of trail mix. Then we can set up two equations:

8x + 4y = 37 (equation 1)

3x + 2y = 15 (equation 2)

We can solve for x and y by using the substitution method. Solve equation 2 for y:

y = (15 - 3x) / 2

Substitute this into equation 1:

8x + 4((15 - 3x) / 2) = 37

Simplify and solve for x:

8x + 30 - 6x = 37

2x = 7

x = 3.5

Now we can substitute x = 3.5 back into equation 2 to find y:

3(3.5) + 2y = 15

10.5 + 2y = 15

2y = 4.5

y = 2.25

Therefore, the cost per pound of jelly beans is $3.50 and the cost per pound of trail mix is $2.25.

Answer 2

Let's use "j" to represent the cost per pound of jelly beans, and "t" to represent the cost per pound of trail mix.

From the first sentence of the problem, we can write an equation for the total cost of 8 pounds of jelly beans and 4 pounds of trail mix:

8j + 4t = 37

From the second sentence of the problem, we can write an equation for the total cost of 3 pounds of jelly beans and 2 pounds of trail mix:

3j + 2t = 15

Now we have two equations with two variables, which we can solve using algebra.

Multiplying the second equation by 4, we get:

12j + 8t = 60

We can now use the first equation to solve for one of the variables in terms of the other. Solving for j, we get:

j = (37 - 4t)/8

Substituting this expression for j into the second equation, we get:

3(37 - 4t)/8 + 2t = 15

Multiplying both sides by 8 to eliminate the fraction, we get:

111 - 12t + 16t = 120

4t = 9

t = 2.25

Substituting this value for t into the expression we found for j, we get:

j = (37 - 4(2.25))/8 = 2.125

Therefore, the cost per pound of jelly beans is $2.125 and the cost per pound of trail mix is $2.25.