Question 1

please someone help me....I am homeschooled and i don't know how to solve these questions....so please can someone tell me how to solve these questions..I will be really grantfull to you even if you just helped me out in only one question!!..thanks

1.Mary's age is 2/3 that of Peter's.Two years ago Mary's age was 1/2 of what Peter's age will be in 5 years' time.How old is Peter now?

2.A half of what John's age was 4 years ago is equal to one third of what it will be in 5 years' time.How old is John now?>>>thanks<<<

Accepted Answer

Define m as Mary's age, p as Peter's age, convert the problem into algebra notation.

1.Mary's age (m) is(=) 2/3 that of Peter's((2/3)*p).Two years ago Mary's age(m-2) was(=) 1/2 of what Peter's age will be in 5 years' time[(1/2)*(p+5)].How old is Peter now?

Get two equations...
m=(2/3)*p, and
(m-2)=(1/2)*(p+5), multiply 2nd eqn by 2 to eliminate fraction, so system is

m = (2/3) p
2m - 4 = p + 5, substitute value of m from 1st eqn into 2nd eqn, get

2((2/3)p) - 4 = p + 5, solve for p... simplify multiplication first

(4/3)p - 4 = p + 5, add 4 to both sides, get

(4/3)p = p + 9, subtract p from both sides, get
(1/3)p = 9, multiply both sides by 3 to eliminate fraction, get
p=27, Peter is 27 years old.

2.A half of what John's age was 4 years ago[(1/2)(j-4)] is(=) equal to one third of what it will be in 5 years' time[(1/3)(j+5)].How old is John now?

(1/2)(j-4) = (1/3)(j+5), I would multiply both sides by 6 to eliminate all the fractions... get
3(j-4) = 2(j+5), work through distributive property
3j - 12 = 2j + 10, add 12 to both sides
3j = 2j + 22, subtract 2j from both sides
j = 22

Question 2

I am having a lot of trouble solving these types of problems on the "Age word problem" questions. Could someone help me with this?
Here's an example:
Kevin is 3 years older than Daniel. Two years ago, Kevin was 4 times as old as Daniel.
How old is Daniel now?

Accepted Answer

let k=kevins age now
let d=daniels age now
k=d+3, kevin is 3 yrs older than daniel now.
2 years ago, kevin was k-2 years old, daniel was d-2 years old, and kevin was 4 times daniels age:
(k-2)=4(d-2), which becomes k-2=4d-8 then k=4d-6. we also know k=d+3 since kevin is 3 years older than daniel now. if you substitute for k, then 4d-6=k=d+3.
4d-6=d+3, 3d=9, d=3.
daniel is 3 years old now.
hope this helps

Question 3

How do i solve this problem, please help
The sum of the ages of Jennie and Matt is 40. Jennie is 5 less than twice Matt's age. How old is Matt?

Accepted Answer

First, you would want to read it over and think of a way to convert this into an equation. so let's say Jennie's age is j and matt's age is m. Jennie's age is 5 less than twice matt's age so jenny's age(j)=2m-5. Jenny's and matt's ages add up to 40 so we know that jenny's age is 
2m-5 and matt's age is m so 2m-5+m=40.
2m+m-5=40 lets get rid of the 5 so add 5 to both sides
2m+m=45
3m=45 (because 2m+m = 2m+1m=3m)
what times 3 is 45? divide both sides to find out
m=15 Matt is 15 years old. Jenny is 25.

Question 4

Kevin is 3years older than Daniel. Two years ago, Kevin was 4times as old as Daniel.

How old is Kevin now?

Accepted Answer

Well, to solve it logically, I would say, for Kevin’s age to be 4 times as much as Daniel, while the age difference is 3, is when Daniel is 1 years old and Kevin is 4. And so, Kevin’s current age is 4 + 2 which is 6.

Question 5

i had my equation the other way around so :
a+40=11a
a-11a=11a-11a
a+40-40-11a=-40
a-11a=-40
-10a=-40
-10a/-10a=-40/-10a
a=4
Although the answer is correct would the working out matter?

Accepted Answer

There are often many correct says to solve an equation.  You can see this in your work.  That's ok.  The properties of equality are very flexible.  As long as you use opposite operations to move items across the equals symbol, the order that you apply your steps doesn't matter.  Though, sometimes you can create more work for yourself like you did.  You did in 3 steps what you could have done in 2 steps.  There is no need to isolate the variable on the left side of the equation because a=4 and 4=a mean the same thing.  Given that the term on the right already contained "a" and was by itself, the faster way to solve the equation is to move all a's to the right side by subtracting "a" from both sides.  Then, you just need to divide by 10.

Question 6

Hi everyone, may be I missed smth, but why, for instance, if somebody in 16 will be as 3 times older as he now,  his age at this moment is 8 by an equation like this b+16=3b? If I've reached now eight years old, so, my age times 2 is sixteen, not times three. So, in 16 I'll be as 2 times older as I now. Right? Is in this case some mentality difference of understanding of English or problems of my math understanding?

Accepted Answer

Sounds like the problem is asking you to compare your current age with your age 16 years into the future.  You have the equation equation:  b + 16 = 3b

b = your current age NOW, in 2018 
In 16 years, your age becomes b+16      
If your current age = 8, then in 16 years, your age = 8+16 = 24
Does 24 = 3 times your current age?  Yes!  3*8 = 24.

In your analysis, you are only going 8 years into the future, not 16 years.  The problem isn't saying your future age is 16, it is saying "your age in 16 years".

8th grade (Eureka Math/EngageNY)

Course: 8th grade (Eureka Math/EngageNY) > Unit 4

Age word problem: Imran

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