Help! Word Problem

Question

A library offers free tutoring after school for children in grades 1-5. The number of student who attend on Friday ws half the number who attended on Thursday. How many students came for tutoring each day if the total number of students served on both days was 42?

Answer 1

Jennifer,

 

We are told that Friday the library had half as many students as on Thursday and that in all there were 42 total from both days. If we call the number of students from Friday n that makes the number of students on Thursday 2n. The total 42 is equal to n + 2n or 3n. One third of 42 is 14, so their were 14 students on Friday, and 28 students on Thursday.

 

n (Friday) + 2n (Thursday) = 42

3n (both days) = 42

n (Friday) = 42/3

n (Friday) = 14

2n (Thursday) = 28

Answer 2

Hey Jennifer,

 

To solve these problems, it's best to try and get the 2 variables down to one variable. In this word problem, we have 2 unknown numbers; the number of students on thursday, lets call that (T) and the number of students on friday, lets call that (F). Now, it gives us a little information ...

 

First, it tells us that the number of students that came on Friday (f) was one half (1/2) of the number of students that came on thursday. To put that in an equation, we'll write:

F=1/2T

 

Next, we know that the total number of students during both days (T+F) was equal (=) to 42. To put that in an equation, we'll write:

F+T=42

 

NOW, to change these 2 variable equations to 1 variable equations, we'll solve for one of the variables. Let's pick F. (you can pick T too if you want)

 

Given F+T=42

to solve for F, we just subtract T on both sides. We end up with F=42-T

 

Plug that in for T in the first equation (F=1/2T), you get

42-T=1/2T

T=28

 

F=(1/2)(28)

F=14

 

These will get a lot easier with more practice!

 

Hope this helps,

Nikita

 

Answer 3

Hi Jennifer! You could solve this a few ways. I'd suggest setting up an equation. Let's write out what we know from the word problem first.

 

Students on Friday = 1/2 (students on Thursday)

 

So for example, if 20 students attended Thursday, then 10 would have attended on Friday, or (1/2)*20

 

With that in mind, let's set an equation up with variables now. 

 

Thursday's students = x

Friday = (1/2)x

 

We know that the total number of students both days was 42, so added together, that should be the answer.

 

x+(1/2)x=42

 

Fractions can be tricky, so let's just get rid of them. We'll multiply every thing by 2 to do so - this is because 2 is the reciprocal of 1/2 and will cancel it out. Remember you need to do this on both sides of the equation!

 

2x + 2(1/2)x=2(42)

 

That will give us...

 

2x+x=84

 

Now it's easier to solve! We'll combine our x variables, then divide to solve for x. 

 

3x=84

 

3x/3 = 84/3

 

x=28

 

We're halfway there now! But remember, x isn't all we need. x represents the number of Thursday students. 

 

Thursday's students = 28
Friday = (1/2)x

 

If we plug 28 in for Friday, we'll find that (1/2)28=14

 

So 14 students attended on Friday.

 

Before you finish - we'll check our answer. 

 

28 students Thursday + 14 students Friday = 42 students total

 

I hope that's helpful! Let me know if you have additional questions!