I dont get it?

Question

Okay i have this homework, i asked for help yesterday.

I got it for a while but i dont get it now.

How do i understand problems like these. . .they are so hard!?

Don is twice as old as Irene; Ed is 16 years older than Irene. The sum of all three of their ages is 60 years. Find the age of each person.

Irene is_____years old, Don is_____years old, and Ed is_____years old

Or how about this one?

Alice is ten years less than twice as old as Bonnie. If the sum of their ages is 26 years, find their ages.

Bonnie is____years old, and Alice is_____years old.

I just dont know how to figure them out, or where to even begin.

Answer 1

These types of problems are teaching you to translate word problems into mathematical equations with multiple variable and then solve the equations simultaneously.

Start with
Don is twice as old as Irene; D is Don, I is Irene
D=2*I

Ed is 16 years older than Irene. E is Ed
E=I+16

The sum of all three of their ages is 60 years.
D+I+E=60

do you see how each statement became an equation?

Now solve. Let's solve for Irene since D and E appear without coefficients. Plug the first two equations into the third:

2*I+I+I+16=60
simplify using algebra
4*I=60-16
I=44/4
Irene is 11 years old.
Using the first and second
Don is 22 and Ed is 27
check:
22+11+27=60

The second one
Alice is ten years less than twice as old as Bonnie. A is Alice and B is Bonnie
A=2*B-10
If the sum of their ages is 26 years
A+B=26

Notice that you have to have as many equations as variables
substitute the first into the second
2*B-10+B=26
3*B=36
B=12
A=14

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Answer 2

Begin by assigning a letter to one of the ages. If one age is twice another, choose the lower age. Then look at the component statements in the question, and write down formulae in terms of the letter chosen for all the ages. Obtain an equation, solve it, and substitute the solution in each of the formulae you have already written down for the different people's ages.

============================

Let Irene's age be a yr ................(1)

Don is twice as old as Irene
Don's age is therefore 2a yr.......(2)

Ed is 16 years older than Irene.
Ed's age is therefore a + 16 yr....(3)

The sum of all three of their ages is 60 years.
a + 2a + a + 16 = 60.
(1 + 2 + 1)a + 16 = 60
4a + 16 = 60
Subtract 16 from each side:
4a = 60 - 16
4a = 44
Divide by 4:
a = 11.

Now use (1), (2) and (3) to find the ages:
Irene is 11, Don is 2 * 11 = 22, and Ed is 11 + 16 = 27.

====================

Let Bonnie's age be b yr ............(4)

Alice is ten years less than twice as old as Bonnie.
Alice's age is 2b - 10 yr ...............(5)

Thesum of their ages is 26 years.
b + 2b - 10 = 26
(1 + 2)b - 10 = 26
3b - 10 = 26
Add 10 to each side:
3b = 36
Divide by 3:
b = 12

Work out the ages from (4) and (5):
Bonnie is 12
Alice is 2*12 - 10 = 24 - 10 = 14.

Answer 3

it makes it easier when you give variables/values to look at...so for the first one irenes age will be X don is 2ce as old, so dons age is 2X, ed= X+16, now add all the ages together because they gave it to you, and you get 60. 2X+X+X+16=60 and solve for x which will be irenes age. simple algebra will reveal irene is 11 don is 2 times that so 22 and ed is 11+16=27
write it out and look at it and it will be a lot easier

Answer 4

This is algebra in a word problem. The constant here is Irene (i).
d=2i
e=i+16
so, i+d+e=60 right?! substitute d and e for the above and find the sum, add them all up, i+2i+(i+16)=60 solve for i
4i+16=60 minus 16 from both sides to yield 4i=44, then divide both sides by 4 to isolate the i, which is i=11.
Irene is 11
Don is 22
Ed is 27
11+22+27=60 checked and correct! :)
---------------------------------------
a=2b-10
b+(2b-10)=26
3b-10=26 +10 to both sides
3b=36 divide both sides by 3
b=12
Bonnie is 12
Alice is 14

let me know if you need more help, I love this stuff :)

Answer 5

60(sum of all ages is the answer)=2x+x+(x+16)
let don be 2x
let irene be x
let ed be x+16
then solve.
60=4x +16
44= 4x
x = 11(irene)
2x= 22(don)
x+16= 27 (ed)

2b-10+b=26
can you do the rest?

Answer 6

2.
26-10=16 bonnie
16/2=8 alice