40% of Amy's stamps is equal to 75% of Mary's stamps. After Mary has given 25% of her stamps away , Amy has 90 more stamps than Mary.
Find the total number of stamps they have at first
.4a = .75m
.75m = a-90
Now just find a and m, and thus a+m
mary's stamps --- m
Amy's stamps ---- a
.4m = .75a
40m = 75a
m = 75a/40 = 15a/8
after giveaway
Mary has .75m
Amy has a + .25m
a + .25m - .75m = 90
a - .5m = 90
2a - m = 180
2a - 15a/8 = 180
16a - 15a = 1440
a = 1440
m =2700
check my arithmetic
Hmmm. I get
a=150
m=80
check:
40% of 150 = 60
75% of 80 = 60
80-20 = 60
150 = 60+90
Extra credit: where did Reiny go wrong?
looks like I can't tell Mary and Amy apart.
To solve this problem, let's assign variables to the number of stamps Amy and Mary have at first.
Let's say Amy initially has "A" stamps, and Mary initially has "M" stamps.
According to the problem, "40% of Amy's stamps is equal to 75% of Mary's stamps." This can be expressed as the equation: 0.4A = 0.75M.
Next, we're told that "After Mary has given 25% of her stamps away, Amy has 90 more stamps than Mary." This can be expressed as the equation: A = M - 0.25M + 90.
Now we can solve this system of equations to find the values of A and M.
Substituting the value of A from the second equation into the first equation, we have:
0.4(M - 0.25M + 90) = 0.75M
Simplifying the left side:
0.4(0.75M + 90) = 0.75M
0.3M + 36 = 0.75M
Rearranging the equation:
0.75M - 0.3M = 36
0.45M = 36
Dividing by 0.45:
M = 36 / 0.45
M = 80
Now that we know M = 80, we can substitute this value back into one of the earlier equations to find A:
A = M - 0.25M + 90
A = 80 - 0.25(80) + 90
A = 80 - 20 + 90
A = 150
Therefore, Amy initially has 150 stamps and Mary initially has 80 stamps.
To find the total number of stamps they have at first, we simply add their individual totals:
Total number of stamps = Amy's stamps + Mary's stamps
Total number of stamps = 150 + 80
Total number of stamps = 230
So, the total number of stamps Amy and Mary have at first is 230.