1)
a raccoon, a cat, and a fox have weights in the ratios 5:3:8 respectively. If their combined weights is 48 lb how heavy is the raccoon?
2) and 3)
1.
Let's call the unknown scale factor "s".
Now we can make this equation:
5s + 3s + 8s = 48 lb
16s = 48 lb
s = 48/16 lb
s = 3 lb
And the weight of the raccoon = 5s = 5*3 = 15 lb
2.
Let's call the number of nickles "n" and the number of dimes "d".
Now we can make these equations:
n + d = 48
5n + 10d = 390
Solve the first one for n (or d) and substitute.
n = 48 - d
5(48 - d) + 10d = 390
240 - 5d + 10d = 390
5d = 390 - 240
d = 150/5 = 30
n = 48 - 30 = 18
3.
Let's call the number of Mommy fish "y" and the number of Mama fish "a".
Now we can make these equations:
y + a = 10
220y + 480a = 2460
Solve the first equation for y (or a) and substitute.
y = 10 - a
220(10 - a) + 480a = 2460
2200 - 220a + 480a = 2460
260a = 2460 - 2200
a = 260/260 = 1
y = 10 - 1 = 9
There were 9 Mommy fish, so there were 220*9 = 1980 Mommy fish eggs, just like you found! :)
1.
Let's call the unknown scale factor "s".
Now we can make this equation:
5s + 3s + 8s = 48 lb
16s = 48 lb
s = 48/16 lb
s = 3 lb
And the weight of the raccoon = 5s = 5*3 = 15 lb
2.
Let's call the number of nickles "n" and the number of dimes "d".
Now we can make these equations:
n + d = 48
5n + 10d = 390
Solve the first one for n (or d) and substitute.
n = 48 - d
5(48 - d) + 10d = 390
240 - 5d + 10d = 390
5d = 390 - 240
d = 150/5 = 30
n = 48 - 30 = 18
3.
Let's call the number of Mommy fish "y" and the number of Mama fish "a".
Now we can make these equations:
y + a = 10
220y + 480a = 2460
Solve the first equation for y (or a) and substitute.
y = 10 - a
220(10 - a) + 480a = 2460
2200 - 220a + 480a = 2460
260a = 2460 - 2200
a = 260/260 = 1
y = 10 - 1 = 9
There were 9 Mommy fish, so there were 220*9 = 1980 Mommy fish eggs, just like you found! :)