Question

a grocery store has 12 lb of trail mix that is 10% banana chips. The store's manager would like to add banana chips to bring the new mix up to 25% banana chips. write and solve a system of equations to find out how many pounds of banana chips manager needs to add.

Answer 1

10% of the 12 lb mix is banana chips, which comes out to 1.2 lb of banana chips. If
`b` is the amount of banana chips the manager will add to the mix, then the new mix's total weight would be
`12+b`, and the manager wants 25% of this to consist of banana chips. This means the final amount of banana chips,
`1.2+b`, should come out to 25% of
`12+b`. In other words,

`(1.2+b)/(12+b)=0.25\implies b=2.4`

so the manager should add 2.4 lb of banana chips.

Answer 2

Let's denote the additional amount of banana chips that the manager needs to add as `x`. So, we need to find out the value of `x`.

We can set up two equations based on the problem.

The first equation represents the total weight of the trail mix after the addition of the banana chips. That would be the original weight of the trail mix (12 lb) plus the additional banana chips (x lb). We can write this equation as:

total_trail_mix = 12 + x

The second equation is defined by the weight percentages given in the problem. According to the problem, the weight of the banana chips in the mix after the additions will be equal to the weight of the original banana chips (which is 10% of the original 12 lb) plus the added banana chips (x lb). It's also given that this is equal to 25% of the total mix after the addition. So, we can write the second equation as:

0.10 * 12 + x = 0.25 * (12 + x)

Now, let's solve this system of equations.

First, you want to isolate x on one side of the equation in the second equation:

0.10 * 12 + x = 0.25 * (12 + x)

When you simplify this, you notice that you have x on both sides. The easiest way to solve for x in this situation is to subtract x from both sides:

0.10 * 12 = 0.25 * 12 - 0.15 * x

Then, to solve for x, divide both sides by -0.15:

x = (0.10 * 12 - 0.25 * 12) / -0.15

By solving this, you find out that the manager needs to add approximately 2.4 lb of banana chips to bring up the new mix to 25% banana chips.