Question

There were n signers of the Declaration of Independence. The oldest was Benjamin Franklin, who was y years old.

7 is 10% of y and n is 80% of y. How many signers were there?

Answer 1

There were 56 signers.

Explanation:

First, set up the two equations for the two situations we are given.

7 is 10% of y . . . . .(1):

`7 = (10)/(100)(y)`

n is 80% of y . . . . .(2):

`n = (80)/(100)(y)`

Now, solve for y in the 1st equation, and substitute y in the second equation to solve for n.

`7 = (10y)/(100)`

`700 = 10y\\`

`70 = y`

`n = (80*70)/(100)`

`n = (5600)/(100)`

`n = 56`

Answer 2

• 56 signers

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7 is 10% of y, find y:

• 7 = 0.1y ⇒ y = 70

n is 80% of y, find n:

• n = 0.8y = 0.8*70 = 56