A math puzzle from before Britain went decimal

[snoozy]

So, I just finished watching "Made in Dagenham", the movie about the women machinists in Ford's factory in Dagenham who struck for equal pay in 1968. At the end of the movie, the govt Employment Secretary announced that with a pay rise of 7 pence, the women would now be at 92% of the mens' payrate.

I thought, there's a math puzzle: knowing that 7p brings them to 92%, what is the mens rate, and what was the women's rate?

As a separate issue, I realized that in those days, the pound was not decimal, but they had the whole shillings and pence thang, which I've never had to deal with, since I first visited England after they went decimal.

So, can anyone tell me (and show me how they figured it) what the answer is?

[Verdant]

Let w = the women's original payrate (prior to the 7p raise)
Let m = the men's payrate

Use the information provide we find

w + 7 = .92 m (Add 7p to the women's payrate equates to 92% of the men's)


So we have one equation and two unknowns. We need more information to correctly answer your question. Essentially, you need as many equations as you have unknowns to solve algebraically.

We could re-arrange the one formula we have to a more classical format with one variable isolated on one side at get:


m = (w + 7) / .92

Now this creates a line on a two-dimension Cartesian coordinate plane that would have an infinite number of correct answers. However, we can assume that both the women's payrate and the men's payrate were integer (whole) numbers so this reduces the plausible answer set into something we can look at more realistically.

Correct integer answer would include
w m
16 25
39 50
62 75
85 100
108 125
131 150
... ...

You can easily see this for yourself by plugging the formula above into a spreadsheet like Excel and looking for the integer answers.

The women's new pay would then add the 7p raise to be 92% of the men's pay
23p to 25p
46p to 50p
69p to 75p
and so on.

[uncle Will in In.]

Was that the last raise the poor old soul got? What kind of retirement plan did she have?

[alpacaspinner]

Algebra was never my subject, so I can't answer your question, but I lived, and went to school, in Ireland for for several years in the '60's, and became quite familiar with the pounds/shillings/pence thing. 1 pound = 20 shillings; 1 shilling = 12 pence; Therefore 1 pound = 240 pence.
The short form for the old pence, by the way, was "d", and not "p" - as in "7d raise" (although I think the English say "rise"). They use "p" now to differentiate from the old pennies.

[snoozy]

Originally Posted by Verdant

Let w = the women's original payrate (prior to the 7p raise)
Let m = the men's payrate

Use the information provide we find

w + 7 = .92 m (Add 7p to the women's payrate equates to 92% of the men's)


So we have one equation and two unknowns. We need more information to correctly answer your question. Essentially, you need as many equations as you have unknowns to solve algebraically.

We could re-arrange the one formula we have to a more classical format with one variable isolated on one side at get:


m = (w + 7) / .92

Now this creates a line on a two-dimension Cartesian coordinate plane that would have an infinite number of correct answers. However, we can assume that both the women's payrate and the men's payrate were integer (whole) numbers so this reduces the plausible answer set into something we can look at more realistically.

Correct integer answer would include
w m
16 25
39 50
62 75
85 100
108 125
131 150
... ...

You can easily see this for yourself by plugging the formula above into a spreadsheet like Excel and looking for the integer answers.

The women's new pay would then add the 7p raise to be 92% of the men's pay
23p to 25p
46p to 50p
69p to 75p
and so on.

Not so easy for me to see!

If, to make estimation easier, instead of 7 pence, it were 8 pence needed to raise the women's rate to 92% of the men's, then each pence would = 1% of the men's rate, yes? In which case, the women would have been getting 84 pence per hour before the raise, while the men were getting 100. Approximately.

I have no idea what Cartesian anything is. (Isn't it some kind of mineral water?...)

And, to translate into shillings, 100pence would = 8 1/3 shillings, yes?

[snoozy]

Checked with a friend, that would be phrased 8 shillings fourpence.

[jassytoo]

Yep, 8/4d

[wogglebug]

Lsd or £ s d - Pounds, shillings and pence
- e.g. £1/19/11½ = One pound nineteen and eleven pence ha'penny
- actually originally from the currency of the Holy Roman Empire
Libra (hence also the abbreviation lb for pound weight)
solidus
denarius
12 silver denarii to a gold solidus
240 denarii formed from a pound bar or rod of silver, so 20 gold solidus to a libra of silver.

There were other coins.
A farthing ¼d was a quarter-penny
A guinea had become standardised at 21/- £1/1/- Twenty-one shillings
Seen the original illustrations of the Mad Hatter? His hat still had a price ticket tucked into the band, for 10/6 - That was half a guinea.
Pop quiz - How many farthings in a guinea? Easy 1,008

[Tracy Rimmer]

Originally Posted by Verdant

Let w = the women's original payrate (prior to the 7p raise)
Let m = the men's payrate

Use the information provide we find

w + 7 = .92 m (Add 7p to the women's payrate equates to 92% of the men's)
....
and so on.

I think I love you