Algebraic Equations

Question

Hi, I need help with these review problems.

Remember to show all work + let statement. Use an Algebraic Equation for each.

 

1. Ofeila has a certain amount of money. If she spends $12, then she has 1/5 of the original amount left. How much money did Ofelia have originally? 

 

2. Three consecutive integers have a sum of 234. What are the three integers?

 

3. Gilden is reading a book that has 276 pages. He has already read some of it last week. He plans to read 20 minutes tomorrow on his crumpet break. By then, he will be 2/3 of the way through the book. How many pages did Gil read last week?

Answer 1

Hi Cierra;

1. Ofeila has a certain amount of money. If she spends $12, then she has 1/5 of the original amount left. How much money did Ofelia have originally?

 

x=amount of money Ofeila has

x-$12=(1/5)x

Let's eliminate the fractions by multiplying both sides by 5...

5(x-$12)=(5)(1/5)x

5x-$60=x

Let's subtract 5x from both sides...

-5x+5x-$60=x-5x

-$60=-4x

Let's divide both sides by -4...

(-$60)/(-4)=(-4x)/(-4)

$15=x

Let's check our work...

x-$12=(1/5)x

$15-$12=(1/5)($15)

$3=$3

2. Three consecutive integers have a sum of 234. What are the three integers?

 

x

x+1

x+2

(x)+(x+1)+(x+2)=234

x+x+1+x+2=234

3x+3=234

Let's subtract 3 from both sides...

-3+3x+3=234-3

3x=231

Let's divide both sides by 3...

(3x)/3=231/3

x=77

x+1=78

x+2=79

Let's check our work...

77+78+79=234

234=234

 

3. Gilden is reading a book that has 276 pages. He has already read some of it last week. He plans to read 20 minutes tomorrow on his crumpet break. By then, he will be 2/3 of the way through the book. How many pages did Gil read last week?

 

I need to know Gilden's rate of reading in terms of how many minutes-per-page.

Answer 2

I think Vivian has done an excellent job here, and I agree with her assessment of problem 3. The way it is written, it is unsolvable with out more information. However, maybe there was a typo, and it should read: "He plans to read 20 PAGES tomorrow on his crumpet break."  If this were the case then we could represent the situation as:

 

p = pages read last week

2 / 3 of 276 or 2 / 3 * 276 = the total reading that he will have done by the end of his break.

so:

Total reading = p + 20 pages.

 

Filling in:

 

(2/3) * 276 = p + 20

184 = p + 20

Subtract 20 from both sides to isolate p.

184 - 20 = p + 20 - 20

164 = p

p = 164

 

What did p mean?

 

I meant that Gilden read 164 pages last week.

 

Fill back in and check:

 

(2/3) * 276 = 164 + 20

       184 = 184... checks.

 

Keep in mind this all flows from GUESSING that there was a typo, and guessing what that typo may have been.

 

James McLain