How do I set up the correct equations for this age word problem?

[harpazo]

Homework Statement

Set up the correct system of equations in two unknowns.

Relevant Equations

P = 1 + W(11)
P + 9 = 7 + 3(W + 9)

In January of the year 2000, I was one more than eleven times as old as my son Will. In January of 2009, I was seven more than three times as old as him. Note: Do NOT solve. Set up the correct system of equations.

This one can easily throw someone struggling with age word problems into a loop.

Let P = parent

Let W = Will

I think the equations look like this:

P = 1 + W(11)

2009 > 2000 by 9.

P + 9 = 7 + 3(W + 9)

The two equations are

P = 1 + W(11)
P + 9 = 7 + 3(W + 9)

 

[PeroK]

 

[Mark44]

Homework Statement:: Set up the correct system of equations in two unknowns.
Relevant Equations:: P = 1 + W(11)
P + 9 = 7 + 3(W + 9)

In January of the year 2000, I was one more than eleven times as old as my son Will. In January of 2009, I was seven more than three times as old as him. Note: Do NOT solve. Set up the correct system of equations.

This one can easily throw someone struggling with age word problems into a loop.

Let P = parent

Let W = Will

I think the equations look like this:

P = 1 + W(11)

2009 > 2000 by 9.

P + 9 = 7 + 3(W + 9)

The two equations are

P = 1 + W(11)
P + 9 = 7 + 3(W + 9)

Looks OK, and leads to the correct answers (which aren't required here), but you should probably combine terms to get the equations as simple as possible.
Also, it's less confusing to write 11W than W(11), as the latter looks like a function expression.

BTW, even though the problem doesn't ask you to solve the system, you can verify that your setup is correct by going ahead and solving the system. If your solution matches the given information, you can be pretty sure that your setup is correct.

By matching the given info, I mean that the ages of Will and his father match both at the start (in 2000) and 9 years later, in 2009.

 

[harpazo]

I will continue to find their ages on paper.

 

[harpazo]

View attachment 285074

What the heck is this?

 

[FactChecker]

It looks good to me and I like that your equations are as close as you can get to a direct translation of the words in the word problem. After you write it down this way, you can mess around with the equations to solve and simplify them. But start with a direct translation, as you have.

 

[symbolipoint]

Homework Statement:: Set up the correct system of equations in two unknowns.
Relevant Equations:: P = 1 + W(11)
P + 9 = 7 + 3(W + 9)

In January of the year 2000, I was one more than eleven times as old as my son Will. In January of 2009, I was seven more than three times as old as him. Note: Do NOT solve. Set up the correct system of equations.

This one can easily throw someone struggling with age word problems into a loop.

Let P = parent

Let W = Will

I think the equations look like this:

P = 1 + W(11)

2009 > 2000 by 9.

P + 9 = 7 + 3(W + 9)

The two equations are

P = 1 + W(11)
P + 9 = 7 + 3(W + 9)

The analysis and created equations are good. Each variable is set as for year 2000.

 

[PeroK]

What the heck is this?

It's a painting called The Scream, by Norwegian artist Edvard Munch. It symbolises my reaction when I realized you are nycmathguy in disguise.

 

[Delta2]

@PeroK seems to me you seeing ghosts again, when was it that you thought a user was a bot while in fact he wasn't...

 

[MidgetDwarf]

View attachment 285074

Just lmao. just lmao. Thank you for giving a chuckle at a least expected place.

 

[harpazo]

It's a painting called The Scream, by Norwegian artist Edvard Grieg. It symbolises my reaction when I realized you are nycmathguy in disguise.

What is nycmathguy? Is this a movie?

 

[Vanadium 50]

What is nycmathguy?