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- Thread starter mathbear
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Please share the context of this problem.I can’t get a clue of this question, could anyone please help? Thank you.

What is being taught in the class - what is the topic? The problem can be solved using principle of simultaneous equation - but that may not be expected from 10 yr olds!

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Hi mathbear. Has your 10-year-old learned how to solve equations? Does she have experience substituting one expression for another? We can answer this exercise using such steps.2B = 3∑

4∑ = 2B + ∂ +1

2∂ + 3∑ = 3B

I'll use choice

∂ + 1 < ∑

Notice that inequality

Which of the given equations contain those symbols? Not the first one, but the other two do:

4∑ = 2B + ∂ +1

2∂ + 3∑ = 3B

We would like to eliminate symbol B from either of those equations, in order to obtain an equation containing symbols ∂ and ∑ only . The easiest way is to make a substitution for 2B because they've already given us an expression for 2B in terms of symbol ∑. The first given equation tells us that 2B is the same amount as 3∑. Therefore, we may substitute the expression 3∑ for 2B anywhere it appears. Let's make that substitution in the second given equation:

4∑ = 2B + ∂ +1

becomes

4∑ = 3∑ + ∂ +1

Next, we would like to put this new equation into the same form as inequality

4∑ – 3∑ = 3∑ + ∂ +1 – 3∑

Simplify:

∑ = ∂ + 1

Now, choice

∑ > ∂ + 1

But we've already shown above (by substitution and solving for symbol ∑) that:

∑ = ∂ + 1

Therefore, inequality

These are the sorts of steps that need to be done, in order to eliminate the given choices until we find the one that's true.

If your 10-year-old understands my example, then have her experiment solving equations for a symbol and making substitutions in other equations. Sometimes, we may need to make substitutions in two equations or solving each for a specific symbol, or make two substitutions in a single equation. The goal is to match the form of given choices, to see whether each is true or false.

If she needs more help, please have her post her efforts or ask specific questions. Thank you!

[imath]\;[/imath]

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Hi there,I can’t get a clue of this question, could anyone please help? Thank you.

I would like to offer another approach you might adopt.

If we number the equations thus:-

Now, since we know (from Equation

So we may now re-write the equations as:-

Now, looking at the 'new' equations…

What does the new Equation

and what does the new Equation

They

If you know what

For example, this knowledge will let you discount Statement

It also allows you to say that Statement

(Because

Do you see why?

If you can follow this reasoning then you should be able to eliminate four of the five statements as not

I will leave it to you to figure out which ones are which but, if you get really stuck, let us know what you have managed to deduce and we will help you complete the process.

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