Jenny's tokens: How meany seconds would it take to get 5,00 tokens?

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Sep 5, 2018
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My math qoustion is,

"Jenny downloaded an app where she can watch videos and earn cash, she gets awarded tokens for every video that she waches. She can cash in her tokens for a 5$ paypal cash. She needs 5,000 tokens for that 5$ paypal cash. She constantly wachses videos. Every 30 seconds she gets 2 tokens so,
How meany seconds would it take to get 5,00 tokens?
 
My math qoustion is,

"Jenny downloaded an app where she can watch videos and earn cash, she gets awarded tokens for every video that she waches. She can cash in her tokens for a 5$ paypal cash. She needs 5,000 tokens for that 5$ paypal cash. She constantly wachses videos. Every 30 seconds she gets 2 tokens so,
How meany seconds would it take to get 5,00 tokens?

Come on. Give it a go. Surely you can count it up.


Hint: \(\displaystyle 5000\;tokens * \dfrac{30\;seconds}{2\;tokens}\)
 
You could set up a proportion, using symbol x to represent the unknown number of seconds they ask for. There's also another way to think about it, using a rate to see a pattern.

If you're in algebra class, then maybe you're supposed to write and solve an equation. Here's a worked example that's similar, using a proportion. If I eat 4 apples per 30 days, how many days do I need to eat a dozen apples?

Let x = the number of days it takes to eat 12 apples

4 apples per 30 days is a rate

12 apples per x days is the same rate, yes? (I haven't changed how fast I'm eating apples; I'm just writing the rate in an equivalent way.) Because the rates are equal, I can write a proportion.

\(\displaystyle \dfrac{4}{30} = \dfrac{12}{x}\)

Solve for x.

Using the rule I learned in prealgebra (for solving proportions when you know three of the four numbers), I multiply on the diagonal and divide by the number not used.

x = (30 × 12) / 4

4 goes into 12 three times, so x = 30 × 3

I need 90 days, to eat a dozen apples (at the rate of 4 apples every 30 days).

You could set up and solve a proportion for your exercise similarly.


There's also an alternate rule for solving proportions.

a/b = c/d means a∙d = b∙c

4/30 = 12/x means 4x = 30(12)

Divide each side by 4. This way is basically the same as what I did above using the prealgebra rule.


With proportions, you can also switch to using reciprocals.

30/4 = x/12

Reduce 30/4 and then multiply each side by 12.

I get x = 6(15)




If you haven't learned about proportions or you're not yet solving equations in beginning algebra, then here's another way: 2 tokens per 30 seconds

2/30 reduces to 1/15

So, the rate at which Jenny gets tokens may also be expressed as: 1 token per 15 seconds

We need the time for 5,000 tokens. Writing out simpler forms of what you're asked to find, is often a good way to consider word problems. Let's write some times for smaller token numbers.

1 tokens : 15sec
2 tokens : 15sec + 15sec
3 tokens : 15sec + 15sec + 15sec
4 tokens : 15sec + 15sec + 15sec + 15sec

The pattern is easy to see. We need the same number of 15-second intervals as tokens.

If we want 4 tokens, we need 4×15 seconds.

If we want 100 tokens, we need 100×15 seconds.

What if we want 5000 tokens? 8-)
 
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