i’m having trouble with this problem that i found on the internet.

Question

When Michael and his 3 friends go to the movies, they each either skate to the theater or ride a bike. The number of wheels in the group as they go to the theater is given by the equation W = 8s + 2b, where S is the number of friends skating and B is the number of friends biking.

if Michael decides to skate and his friends decide to bike, how many videos are in the group?

If everyone decides to skate, how many wheels are in the group?

In the equation W = 8s + 2b, explain why the variable S has a coefficient of 8 and the variable who has a coefficient of 2.

suppose that has Michael and his 3 friends go to the movies, there are 26 wheels in the group. How many are on skates and how many are riding a bike?

Answer 1

I think you have a few typos in your problem, but that's OK -- probably autocorrect? But let's assume that I've understood what words should have been there.

First off, let's look at the equation W = 8s + 2b . The number 8 (the coefficient of s) is saying that if one person skates, they will be using 8 wheels (presumably, they use 2 skates and each skate has 4 wheels). The number 2 is saying that if one person bikes, they will be using the 2 wheels on the bicycle.

So, in the first example, Michael skates and his three friends bike. So, s is 1 (1 person skating), b is 3 (3 people biking), and the total number of wheels W is 8 + 2 · 3, or 8 + 6 = 14 wheels (I'm assuming the word "videos" is a typo and should have been "wheels"?).

If everyone skates, there are 4 people, so s is 4 and b is 0, and there are 4 * 8 = 32 wheels.

For the last question, we are not given either s or b directly. But we know that the total of s and b is the 4 people in their group, and the total number of wheels W is 26, so we can write two equations:

s + b = 4

26 = 8s + 2b

Now we need to solve these two equations for s and b. I like to start by simplifying the second equation by dividing it all by 2, and rewriting the first equation so that left/right sides are swapped:

4 = s + b

13 = 4s + b

Now subtract the first equation from the second to get:

9 = 3s or s = 3

Substitute that into the first equation to find out that b = 1 -- so, 3 people skated, and 1 person biked, to get a total of 3 · 8 + 2 = 26 wheels.