1. ## Singapore Math models

I am a parent of a 5th grade child in NC. She is in the Advanced math class. They are using singapore math model approch to word problems and I need help understanding the system.

Here is her word problem for tonight:

The cost of four watched and three chains is $510. The cost of three watches and four chains is$505. What is the cost of 1 chain?

Gary

2. Set up a small system of equations letting w = watch and c = chain.

Then you have:

$\displaystyle 4w+3c=510$

$\displaystyle 3w+4c=505$

Now you have a small system of linear equations in two variables to solve.

Do you or your daughter know how to solve this by elimination or substitution?.

Wow, this is impressive for a 5th grader. You must be proud of her.

3. Hello, Gary!

I'm not familiar with the Singapore Math Model approach.
I'll give you a standard one . . .

The cost of four watches and three chains is $510. The cost of three watches and four chains is$505.
What is the cost of one chain?

Let $\displaystyle W$ = cost of a watch.
Let $\displaystyle C$ = cost of a chain.

The cost of four watches and three chains is $510. . . This is written: .$\displaystyle 4W + 3C \:=\:510$.[1] The cost of three watches and four chains is$505.
. . This is written: .$\displaystyle 3W + 4C \:=\:505$ .[2]

We have a system of equations . . .

$\displaystyle \begin{array}{cccc}\text{Multiply [1] by -3:} & \text{-}12W - 9C & = & \text{-}1530 \\ \text{Multiply [2] by 4:} & 12W + 16C & = & 2020 \end{array}$

Add the equations: .$\displaystyle 7C \:=\:490\quad\Rightarrow\quad C \:=\:70$

Therefore, the cost of one chain is $70. 4. I can handle those. Algebra is what I am used to. I am just lost with the model approach. Originally Posted by galactus Set up a small system of equations letting w = watch and c = chain. Then you have:$\displaystyle 4w+3c=510\displaystyle 3w+4c=505$Now you have a small system of linear equations in two variables to solve. Do you or your daughter know how to solve this by elimination or substitution?. Wow, this is impressive for a 5th grader. You must be proud of her. 5. One possible method watches |-------| chains |----| |-------|-------|-------|-------|----|----|----|$510
|-------|-------|-------|----|----|----|----| $505 Rearrange |-------|-------|-------|----|----|----|-------|$510
|-------|-------|-------|----|----|----|----| $505 Difference between the two bars is difference between one watch and one chain. 510 - 505 = 5 A watch is$5 more than a chain.

4 watches, then, would be the same as 4 chains + 4 x $5, or 4 chains +$20

|----| 5 |----| 5 |----| 5|----| 5|----|----|----| $510 7 chains =$510 - $20 =$490
1 chain = $490/7 =$70