calves of domestic cows and hawaiian monk seal pups both again mass at a constant rate for at least two months from birth. An average calf will weigh 75 pounds on the second day after its birth, and 120 pounds on day 20. An average seal pup will weigh 124 pounds on day 24 and 196 pounds at weaning, day 42. At what age would a calf and a seal pup weigh the same?

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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