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Answer :
Final answer:
To find the age at which a calf and a seal pup would weigh the same, we can set up and solve a system of equations using the given information about their weight gain rates. The age at which their weights are the same is found to be 49 days old.
Explanation:
To find the age at which a calf and a seal pup would weigh the same, we need to set up a system of equations. Let's assume x represents the age in days. From the given information, we can write the equation for the calf's weight as y = 75 + mx, where m is the rate of weight gain per day. Similarly, for the seal pup, the equation is y = 124 + nx, where n is the rate of weight gain per day. To find the age at which their weights are the same, we can set up the equation 75 + mx = 124 + nx and solve for x.
First, let's find the rate of weight gain for the calf: (120 - 75) / (20 - 2) = 45 / 18 = 2.5 pounds per day. Similarly, for the seal pup: (196 - 124) / (42 - 24) = 72 / 18 = 4 pounds per day.
Plugging these rates back into the equation, we have 75 + 2.5x = 124 + 4x. Subtracting 2.5x from both sides, we get 124 - 75 = 1.5x. Simplifying, we find x = 49.
Therefore, a calf and a seal pup would weigh the same at 49 days old.
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