Question

Based on the word problem, define two variables (x and y) and write a system of equations to represent the situation. Then solve your system using the substitution method.

You have recently discovered that you can buy them, in bulk, directly from the manufacturer. You’ve decided to spend every dollar you have on Cheetos and Takis. You’re going to buy a total of 30 bags (Cheetos and Takis combined). The Cheetos cost $15 for a large bag and the Takis cost $40 for a large bag, and you have $750 to spend. How many of each type of snack do you buy?

Answer 1

18 cheetos bags, 12 takis bags

Explanation:

Assigning:

Let x = number of cheetos bag(s)

Let y = number of takis bag(s)

System of Equations:

x + y = 30

15x + 40y = 750

Solving:

Isolate y in first equation : y = 30 - x

Substitute into second equation:

15x + 40(30 - x) = 750,

15x + 1200 - 40x = 750,

-25x = - 450,

x = 18 cheetos bags

y = 30 - 18 = 12 takis bags

Answer 2

the solution for the system is;

`c = 18 \\ t = 12`

Explanation:

Let C be the number of cheetos bags that you will buy and T the corresponding number of Takis bags.

Since you're going to buy a total of 30 bags, then;

`c + t = 30`

Since the Cheetos bag cost $15, then the total cost for C bags is 15C. The same way, since the Takis bag cost $40, the total cost for T bags is 40T. Since you will spend $750, then;

`15c + 40t = 750`

Use the substitution method to solve the system. To do so, isolate one variable from the first equation and substitute the resulting expression into the second equation;

`c + t = 30 \\ c = 30 - t`

Substitute that expression for C into the second equation and solve for T:

`15c + 40t = 750 \\ 15(30 - t) + 40t = 750 \\ 450 - 15t + 40t = 750 \\ 450 + 25t = 750 \\ 25t = 750 - 450 \\ 25t = 300 \\ t = (300)/(25) \\ t = 12`

Substitute back T=12 into the expression for C;

`c = 30 - t \\ c = 30 - 12 \\ c = 18`

Therefore, the solution for the system is;

`c = 18 \\ t = 12`

Which mean that you buy 12 bags of Takis and 18 bags of Cheetos.