Both gardens grew the same way, but Tess's keeper charged a fee.
The big ideaA small fee every year eats more than it looks, because taken coins stop growing.
How it works
Omar and Tess each planted 100 pretend coins and both gardens grew the same way. Tess's garden had a keeper who charged a fee.
A fee is a price for a service, like tending the garden. Each year the keeper took one coin for every fifty inside.
Two coins sounds tiny, but the keeper came back every year, and coins taken stop growing too.
The same gardens, with and without a fee.How far ahead Omar is.
Example 1: How big is the fee?
The keeper takes 1 coin for every 50 inside.
A garden of 200 holds four fifties, and 4 × 50 = 200.
So the keeper takes 4 coins.
Example 2: Year one
Both gardens grow to 110.
The keeper takes 2 coins from Tess: 110 − 2 = 108.
Omar keeps all 110.
Example 3: Year twenty
Omar holds 655 and Tess holds 447.
655 − 447 = 208
Tess is 208 coins behind.
Example 4: The growth the fee ate
Omar's garden grew by 655 − 100 = 555 coins.
Tess's garden grew by 447 − 100 = 347 coins.
555 − 347 = 208
The fee ate 208 coins, more than a third of all the growth.
Words to know
fee
A price for a service, like tending a garden.
keeper
The one who tends the garden and takes the fee.
growth
The new coins a garden adds.
Watch out
Coins taken as a fee stop growing too, so the gap is bigger than the fees: the keeper took only 89 coins, but Tess is 208 behind.
Two coins a year sounds tiny. Twenty years of bites are not small.
A fee can be fair when it pays for real help. Ask how much, how often, and for what.
A fee can still be charged in a year with no growth. Growth is never promised, and these gardens are made up.
Try it
A keeper takes 1 coin for every 50. A garden holds 300 coins. How many coins does the keeper take?
Year one: a garden grows to 110 and the keeper takes 2. How many coins are left?
Year 10: Omar has 256 and Tess has 211. How far ahead is Omar?
Name the three things to ask about a fee.
Answers: 1. 6 coins · 2. 108 coins · 3. 45 coins · 4. How much, how often, and for what
Try at homeWith a grown-up, find a fee they pay for a service, like a membership. How much is it, how often, and what does it get them?
For grown-upsFind a fee a grown-up pays for a service, like a membership, and ask the three questions together: how much, how often, and what does it get them? The gardens here are made up, so keep it about the idea.
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