# [SPLIT/MOVED] 'age', 'money' word probs: can't create eqns

#### what1sth1s

##### New member
1) Cheryl is 26 years older than her daughter Brooklyn. Last year, Cheryl was 2 years older than 7 times Brooklyn's age. How old are Cheryl and Brooklyn now?

What I did was:

Let x+2 be Cheryl's age.
Let 7x be Brooklyn's age.

2) Lisa has twice as many dimes as nickels. If there are 42 coins in total, how much money does Lisa have?

#### jonboy

##### Full Member
Hello What1sth1s !

1) Cheryl is 26 years older than her daughter Brooklyn. Last year, Cheryl was 2 years older than 7 times Brooklyn's age. How old are Cheryl and Brooklyn now?
Hmm you just gotta think about these problems.
We will let Cheryl's age be: $$\displaystyle \L \;x$$

We will let Brooklyn's age be: $$\displaystyle \L \;b$$

Cheryl is 26 years older than her daughter Brooklyn: So $$\displaystyle \L \,x=b+26$$

Last year Cheryl was 2 years older than 7 times Brooklyn's age: $$\displaystyle \L \,x-1=7(b-1)+2$$

Since both are equal set them equal to each other: $$\displaystyle \L \;b+26=7b+2$$

Solve for $$\displaystyle \L \,b$$ and then fill that into one of our original equations with $$\displaystyle \L \,x$$ in it to get both Brooklyn's and Cheryl's age.

2) Lisa has twice as many dimes as nickels. If there are 42 coins in total, how much money does Lisa have?
We will let the number of Nickels be: $$\displaystyle \L \;n$$

We will let the number of Dimes be: $$\displaystyle \L \;d$$

Lisa has twice as many dimes as nickels: $$\displaystyle \L \,n=2d$$

There are 42 coins in total: $$\displaystyle \L \, n+d=42$$

Subsitution: $$\displaystyle \L \,2d+d=42$$

Solve for $$\displaystyle \,d$$ and then plug it back into $$\displaystyle \,n=2d$$ and you will know how many dimes and nickles Lisa had.

#### mcrae

##### Junior Member
let cherls current age be x
let brooklyns current age be b
1) x=b+26

let cheryls age last year be x-1
let brooklyns age last year be b-1
2)x-1=7(b-1)+2
rearrange: x=7b-4

b+26=7b-4
26+4=7b-b
30=6b
b=30/6=5

substitute into 1 and 2 to check they give the same answer for x:
1)x=5+26=31
2)x-1=7(5-1)+2
x-1=7(4)+2
x-1=30
x=31

cherly is 31, brooklyn is 5.

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if she only have dimes nad nickels, and twice as many dimes as nickels, then 2/3 of her coins will be dimes and 1/3 will be nickels.
2/3*42=28 dimes *0.10 cents each = $2.80 1/3*42=14 nickels * 0.05 cents each =$0.70
$2.80+$0.70=\$3.50

#### Denis

##### Senior Member
what1sth1s said:
1) Cheryl is 26 years older than her daughter Brooklyn. Last year, Cheryl was 2 years older than 7 times Brooklyn's age. How old are Cheryl and Brooklyn now?
all i did was:
Let x+2 = Cheryl
Let 7x = Brooklyn

2) Lisa has twice as many dimes as nickels. If there are 42 coins in total, how much money does Lisa have?
Next time, use a new thread for new problems...

1) Cheryl is 26 years older than her daughter Brooklyn. Last year, Cheryl was 2 years older than 7 times Brooklyn's age.

Go easy, step by step:
"Cheryl is 26 years older than her daughter Brooklyn."
B = Brooklyn, C = Cheryl ; then C = B + 26 : ok?

"Last year, Cheryl was 2 years older than 7 times Brooklyn's age."
Last year, Brooklyn = B - 1 and Cheryl = C - 1 : ok?
So C - 1 = 7(B - 1) + 2 : still with me?

C - 1 = 7B - 7 + 2
C - 1 = 7B - 5
C = 7B - 4 : understand?

And since C = B + 26, then:
7B - 4 = B + 26
Can you finish it?

2)Lisa has twice as many dimes as nickels. If there are 42 coins in total, how much money does Lisa have?

Step by step again:
"Lisa has twice as many dimes as nickels."
N = nickels; then dimes = 2N : easy nuff?

"If there are 42 coins in total, how much money does Lisa have?"
N + 2N = 42 : easy again?
Now solve for N, then figure out the total money: .05(N) + .10(2N)