PAULA ,SIMON AND RANDY COLLECTED INSECTS FOR THEIR SCIENCE PROJECT. AT THE END OF THE FIRST WEEK PAULA AND RANDY TOGETHER HAD 89 INSECTS, RANDY AND SIMON TOGETHER HAD 85 INSECTS. HOW MANY DID EACH HAVE ALONE?
P + R = 89
R + S = 85
You need a third equation to solve for all three unknowns. Is that the only information you were given?
RANDY AND SIMON TOGETHER HAD 80
That disagrees with you previous statement "RANDY AND SIMON TOGETHER HAD 85"
When you finally get three independent statements stated as equations, then use algebra to solve them.
To solve this problem, we can use a system of equations. Let's denote the number of insects that Paula, Simon, and Randy have alone as P, S, and R, respectively.
From the given information, we can form the following equations:
1) Paula and Randy had 89 insects together:
P + R = 89
2) Randy and Simon had 85 insects together:
R + S = 85
To solve this system of equations, we can use the method of substitution or elimination. Let's use the method of substitution:
From equation 1), we can isolate P:
P = 89 - R
Substitute this expression for P in equation 2):
(89 - R) + S = 85
Simplify the equation:
S + R = 85 - 89
S + R = -4
Now we have two equations:
1) P + R = 89
2) S + R = -4
To isolate S, let's subtract equation 2) from equation 1):
(P + R) - (S + R) = 89 - (-4)
P - S = 93
Now we have a new equation:
P - S = 93
From this equation, we can isolate P:
P = 93 + S
Substitute this expression for P in equation 1):
(93 + S) + R = 89
Simplify the equation:
S + R = 89 - 93
S + R = -4
We now have two equations:
1) S + R = -4
2) S + R = -4
Since both equations are the same, it means that S and R can be any values, as long as their sum is -4. So, the number of insects that Paula, Simon, and Randy have alone cannot be determined with the given information.