Need help with math problem?

Let s = the weight of one spool, t = the weight of one thimble, and b = the weight of one button.

We know that 7s + t = 55b

And that s = t + b

Since we want to know the relationship between buttons and spools, let's rearrange that second equation to define things in terms of thimbles. Subtract b from each side and you get

s - b = t

Now, take this value of t and substitute it into the first equation

7s + s - b = 55b

Add b to each side and combine the s values

8s = 56b

Divide both sides by 8

s = 7b

7 buttons will balance a spool

Use S for spools, T for thimbles, and B for buttons. Put what you know into equation form:

7S + T = 55B [7 spools and 1 thimble balance 55 buttons.]

S = T + B [1 spool balances 1 thimble and 1 button]

You need to express S in terms of B. [How many buttons will balance 1 spool?]

Use the first equation to express T in terms of S and B by subtracting 7S from both sides:

7S + T = 55B becomes

T = 55B - 7S

Substitute 55B - 7S for T in the second equation:

S = T + B becomes

S = (55B - 7S) + B

Simplify:

S = 56B - 7S

Add 7S to both sides:

8S = 56B

Divide both sides by 8:

S = 56B / 8 = 7B

It takes 7 buttons to balance 1 spool.