xon wrote:
Let a = the number of adults, m = the number of men, w = the number of women, c = the number of children, and t = the total number of people taking part in the race.
The total number of people taking part in the race, t, is 2500. So t = c + m + w.
The number of adults is 4 times c (4*c), so a = 4c.
1.) Replace the variables with the numbers you already know into the equation t = c + m + w and you get...
2500 = c + 1200 + w
If m + w (or 1200 + w), a, is equal to 4c, then you can also say the opposite, that c is equal to 1/4a (or 1/4(1200 + w)).
2.) Substitute 1/4a in the place of c to get...
2500 = 1/4(1200 + w) + 1200 + w
3.) Use the distributive property of multiplication to get...
2500 = 300 + w/4 + 1200 + w
4.) Subtract to get...
1000 = w/4 + w
5.) Multiply both sides by 4 to get...
4000 = w + 4w
6.) Add to get...
4000 = 5w
7.) Divide to get the number of women who took part in the cross country race.
I did this in my head and got to the same answer. It did not involve that many steps. But, hey, I still got the same answer.
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I am a partially verbal classic autistic. I am a pharmacology student with full time support.