A student weighs her hamsters two at a time. Sandy and white ears weigh 209 g together. White ears and sport weigh 223 g together. Sandy and sport weigh 216 together. How much does each hamster weigh?
s+w = 209
w + p = 223 , where p is sport, (already used s)
s + p = 216
s+w = 209 ----> w = 209 - s
w + p = 223 --- w = 223 - p
then 209 - s = 223 - p
p - s = 14
add this to the third equation and it all comes apart nicely
To solve this problem, we can set up a system of equations based on the given information. Let's assume the weight of Sandy is represented by 's', the weight of White ears is 'w', and the weight of Sport is 'p'.
According to the problem, we have the following information:
1. Sandy and White ears weigh 209 g together, so we can write the equation: s + w = 209.
2. White ears and Sport weigh 223 g together, so we can write the equation: w + p = 223.
3. Sandy and Sport weigh 216 g together, so we can write the equation: s + p = 216.
Now, we need to solve this system of equations to find the values of s, w, and p.
One way to solve this system of equations is by the method of substitution. We can solve one equation for one variable and substitute it into the other equations. Let's solve the first equation for 's':
s = 209 - w.
Now substitute this value of 's' into the second and third equations:
(209 - w) + p = 216,
w + p = 223.
Now we have a system of two equations with two variables:
(209 - w) + p = 216,
w + p = 223.
Simplify the first equation:
209 - w + p = 216.
Rearrange this equation by moving the 'p' term to the other side:
209 - w = 216 - p.
Now, subtract the second equation from this result:
(209 - w) - (w + p) = 216 - p - 223.
Simplify:
209 - w - w - p = 216 - p - 223.
Combine like terms:
209 - 2w - p = 216 - p - 223.
Combine constants:
209 - 2w - p = -7 - p.
Rearrange the equation:
209 - 7 = -p + p - 2w.
Combine like terms:
202 = -2w.
Divide by -2:
w = -101.
Since the weight of White ears cannot be negative, we must have made an error somewhere in our calculations. Let's start over and try solving the problem again.
Let Sa = weight of sandy
Let W = weight of white ears
Let Sp = weight of sport
Sa + W = 209
W + Sp = 223
Sa + Sp = 216
Three equations and three unknowns. Solve.