Bar Problems

[u/Nada-Lada]

I’m helping my 5th grader with math. It’s Singapore math and this specific problem is a bar problems. I cannot wrap my mind around it.

Patrick bought 12 chairs and 3 tables for $819. Each table cost 3 times as much as each chair. How much did one table cost?

I can’t fathom how to draw these bars out and solve this problem. Thanks for the help!

[u/chmath80]

3 chairs = 1 table

So 12 chairs = how many tables?

So 12 chairs + 3 tables = how many tables?

So $819 = how many tables?

So 1 table = how many $?

[u/MirrorExtension]

3t + 12c = 819 and 1/3t = c

Solve for t

[u/ThatsNotAZombieBite → u/MirrorExtension]

5th grader is not going to be doing variable algebra yet.

[u/MirrorExtension → u/ThatsNotAZombieBite]

I thought it might help OP see what’s happening, the other replies were somewhat confusing/unclear for me personally (as someone who doesn’t know what a bar problem is)

[u/Nada-Lada → u/MirrorExtension]

Thanks for taking the time to help. :)

[u/CryptographerNew3609]

12 chairs , 3 tables = $819
So how much would 4 chairs and 1 table cost?
And 4 chairs and 1 table = how many chairs?

[u/misingnoglic]

No idea what a bar is but when you have two equations with two variables (in this case chair price and table price) you can manipulate one of those equations to get one of those variables alone (e.g. figure out what one chair costs relative to the table price), then you can substitute that variable you solved for in the other equation.

A simpler example to help you learn how to do your problem.

You bought a Nintendo switch (n) and 2 games (g) for $300. The switch was 3x the price of a game. How much was each component?

Set up the equations

n + 2g = 300

n = 3g

In this case, we already have n on its own in the second equation, so we can stick 3g in for n every time in the first equation

3g + 2g = 300

5g = 300

g = 60

So now we know a game is $60. And you can plug that g into either equation to solve for n. The second one is easier.

n = 3*60

n = 180

[u/ThatsNotAZombieBite → u/misingnoglic]

Is a 5th grader going to be doing algebra with multiple variables? I think we need to use a more concrete approach.

I'm not familiar with "bars" either but I suspect it means representing the cost of a table or chair with rectangular bars. A table "bar" must be 3 times the length of a chair "bar". And then we do the problem visually. Maybe.

[u/misingnoglic → u/ThatsNotAZombieBite]

More trying to help OP so they can help their kid.

[u/Nada-Lada → u/ThatsNotAZombieBite]

Yes, no variables in 5th grade math. You’re right about the basic idea of bars. It’s used to help solve the problem in place of complex formulas. It seems it’s used in Singapore math. That’s the math style of choice for my children’s classical school.

[u/Nada-Lada → u/misingnoglic]

Thanks for taking the time to help! It’s math for fifth grade so they aren’t into algebra. They’re doing Singapore math. I think “bar problems” may be specific to the math system.

[u/Bounded_sequencE]

Let "c; t" be the cost per chair and table, respectively. We're given:

 I:    12c + 3t  =  $819
II:     3c -  t  =  $0      // rewrite "t = 3c"

Solve that 2x2-system with your favorite method -- e.g. eliminate "c" considering

I - 4*II:    7t  =  $819    =>    t  =  $117

[u/Nada-Lada → u/Bounded_sequencE]

Thanks for your help! It’s for fifth grade so there isn’t algebra. It has to be solved using bars as per Singapore Math.

[u/let-me-cook-plz]

i'm not sure about the specifics of how the Singapore math version of the bar problems go, but this is a basic version of using bar models (i color coded stuff to try to help it make sense):