Help, please, with these two Lial's algebra problems...

[Colleen]

Oh, dear. How sad is it that already in the second chapter of Lial's Intro Algebra, I'm unable to solve some of the problems?:001_huh: I didn't purchase the student solutions manual but perhaps I'll need it after all. These two problems come from the section titled "Summary Exercises on Solving Applied Problems", toward the end of Chapter 2. My son was able to solve them using the "bar method" taught in Singapore Math. He should also be able to solve them by writing an equation using a variable expression ~ and that's where we're both drawing a blank. So it's the actual algebraic expressions I need, please.

 

#19) Mr. Silvester is 5 years older than his wife. Five years ago his age was 4/3 her age. What are their ages now?

 

#20) Chris is 10 years older than Josh. Next year, Chris will be twice as old as Josh. What are their ages now?

 

Thanks for helping!:)

[Cathy in TX]

Let X= Mrs. Silvester's age now.

That means Mr.s Silvester's age now = X + 5

 

Here is the equation:

(x + 5) - 5 = 4/3 (x -5)

 

x = 4/3x - 20/3

x - 4/3 x = 4/3 x - 20/3 - 4/3x

-1/3 x = -20/3

-3(-1/3x) = -3(-20/3)

x = 20

x=5 =25

[Cathy in TX]

Okay, I reread your post and saw you just want the algebraic expressions. :001_smile: Here is the second one:

 

x= Josh's age

x + 10 = Chris's age

 

2(x + 1) = (x + 10) + 1

 

(The 1 added on both sides of the above equation represents "next year.")

[Carol in Cal.]

#19) Mr. Silvester is 5 years older than his wife. Five years ago his age was 4/3 her age. What are their ages now?

 

#20) Chris is 10 years older than Josh. Next year, Chris will be twice as old as Josh. What are their ages now?

 

Thanks for helping!:)

 

First you assign the variables, and then you take your information and make it into equations. You need at least as many equations as you have unknowns to be able to solve the problem.

 

So, for the second problem:

 

Chris' age is X.

Josh's age is Y.

 

So we have two unknowns, and thus need at least two equations.

 

Here is the equation relating their ages now:

Y + 10 = X (because Chris is 10 years older than Josh)

 

Here is the expression relating their ages next year:

(X+1) = 2(Y + 1)

 

Notice that I added a year to each of the two ages, to account for the fact that we are looking at their ages next year. Then I multiplied Josh's age next year by 2, because next year his age will be twice what Chris' age is.

 

I think you can take it from here--you just wanted to walk through how to set up the problem, right?

[Colleen]

You need at least as many equations as you have unknowns to be able to solve the problem. So, for the second problem:

 

Chris' age is X.

Josh's age is Y.

 

So we have two unknowns, and thus need at least two equations.

 

Except that at this point in the text, expressions using two variables have yet to be taught. My natural instinct was to use "X" and "Y" as you have, but it justifiably doesn't make sense to my son because he's only learned to solve for one variable. Kwim?:)

[Colleen]

Okay, I reread your post and saw you just want the algebraic expressions. :001_smile: Here is the second one:

 

x= Josh's age

x + 10 = Chris's age

 

2(x + 1) = (x + 10) + 1

 

(The 1 added on both sides of the above equation represents "next year.")

 

I think I get it.:D

[Robin in Tx]

Colleen, I am getting more freaked out all the time by how much of this stuff I've forgotten. I took all sorts of college math (had a partial scholarship for math/engineering!), and I *still* feel like I have to learn this stuff all over again! I've slept WAY too may times since doing this last! LOL

 

Likely, they didn't expect two variables at this point. They probably intended Chris's age to be X, and Josh's age to be X+10.

 

I had to stop and think about this one. Isn't that pitiful?

 

Note to self: order solutions manuals from here on out! :)

 

 

ETA: Okay, now I see that I'm repeating what Cathy already said... sorry I didn't read the whole thread first!

[Colleen]

Colleen, I am getting more freaked out all the time by how much of this stuff I've forgotten. I took all sorts of college math (had a partial scholarship for math/engineering!), and I *still* feel like I have to learn this stuff all over again! I've slept WAY too may times since doing this last! LOL

 

I hear you! I've actually been surprised thus far at how much I do remember. And yet here I am asking for help on such simple problems. Sigh.

 

Likely, they didn't expect two variables at this point. They probably intended Chris's age to be X, and Josh's age to be X+10.

 

No, they didn't expect two variables, I know that because using two variables hasn't even been presented. But the sad truth is that even with X as Chris's age and X+10 as Josh's age, I was stymied all morning as to how to set up the equation. And of course, once I glanced at Cathy's reply it made sense.

 

I'm glad you posted so I know I'm not alone!;)