I need help!

[tribe34]

Can't figure out how to start. Here's the question: When the value of Zachery's nickels is 1/6 the value of his dimes, he will have how many times as many dimes as nickels?

 

[tkhunny]

Rule # 1 - Name Stuff!

Name What?

What does it want?

N = # of Nickles
D = # of Dimes

Now translate the given information into terms of N and D.

"When the value of Zachery's nickels is 1/6 the value of his dimes, "

N*0.05 = (1/6)*D*0.10

"will have how many times as many dimes as nickels"

D = k*N, for k a Whole Number

Now solve.

k = D/N

From our first Equation, we have D/N = 6*0.05/(0.10) = 6/2 = 3

Check it out. It 3 times as many dimes worth 6 times as much as the nickles.

1 nickle - 0.05
3 dimes - 0.30
0.30 / 0.05 = 6

That one works!

One problem for free. You show us the next one. All I really did here was go through it systematically. It wasn't magic.

 

[soroban]

Hello, tribe34!

Since you posted this under Arithmetic,
can I assume you haven't had Algebra yet?

When the value of Zachery's nickels is 1/6 the value of his dimes,
he will have how many times as many dimes as nickels?

We already know that: .one nickel equals \(\displaystyle \frac{1}{2}\) of a dime.
. . That is: .\(\displaystyle 5 \,=\,\frac{1}{2}(10)\)

Then: .one nickel equals \(\displaystyle \frac{1}{6}\) of 3 dimes.
. . That is: .\(\displaystyle 5 \,=\,\frac{1}{6}(30)\)

Therefore, he has 3 times as many dimes as nickels.