Question

1. a 180-pound person burns about 88.5 calories every 15 minutes while bowling. write an equation to represent how many calories a 180-pound person burns every minute. will a 180-pound person or a 120-pound person burn more calories in 2 hours of bowling? explain. write an equation where c represents the number of calories and t represents the time in minutes.

c = 5.9t
(use the operation symbols in the math palette as needed. type an equation. use integers or decimals for any numbers in the equation )

the 180-lb person will burn more calories. a 120-lb person burns □ more calories each minute than a □ person.
(type an integer or a decimal )

Explanation:

Step1: Find calories per minute for 180 - lb

A 180 - pound person burns 88.5 calories in 15 minutes. To find calories per minute, divide 88.5 by 15: $\frac{88.5}{15}=5.9$. So the equation is $c = 5.9t$.

Step2: Assume rate for 120 - lb (proportional)

The rate of burning calories is proportional to weight (assuming similar activity intensity). Let the rate for 120 - lb be $r$. Then $\frac{r}{5.9}=\frac{120}{180}$. Solve for $r$: $r = 5.9\times\frac{120}{180}\approx3.93$.

Step3: Find difference in rates

Subtract the rate of 120 - lb from 180 - lb: $5.9 - 3.93 = 1.97$ (approx). But wait, actually, the problem says "A 120 - lb person burns [x] more calories each minute than a [y] person" – no, wait, 180 - lb has higher rate. Wait, maybe the problem has a typo, but following the rate: 180 - lb rate is 5.9, 120 - lb rate is $\frac{88.5\times120}{180\times15}$? Wait no, original: 180 - lb: 88.5 cal/15 min = 5.9 cal/min. For 120 - lb, since weight is 2/3 of 180, the rate should be 2/3 of 5.9? Wait no, actually, the problem is asking "A 120 - lb person burns [ ] more calories each minute than a [ ] person" – no, 180 - lb burns more. Wait, maybe the intended is to find how much less 120 - lb burns, but the problem says "more" – maybe a mistake, but let's recast. Wait, the rate for 180 - lb is 5.9, for 120 - lb: let's recalculate the rate correctly. The formula for calories burned in activity is often proportional to weight. So if 180 - lb burns 88.5 in 15 min, then 120 - lb burns $\frac{120}{180}\times88.5$ in 15 min, so per minute: $\frac{120}{180}\times5.9=\frac{2}{3}\times5.9\approx3.93$. Then the difference is $5.9 - 3.93 = 1.97\approx2.0$? Wait, no, maybe the problem is that the user made a mistake, but let's do it properly.

Wait, the problem says "A 120 - lb person burns [ ] more calories each minute than a [ ] person" – but actually, 180 - lb burns more. So maybe the dropdown is 120 - lb and the other is 180 - lb? No, the first part: "The 180 - lb person will burn more calories." Then "A 120 - lb person burns [x] more calories each minute than a [y] person" – no, that's incorrect. Wait, maybe the problem has a typo, but following the rate: 180 - lb rate is 5.9, 120 - lb rate is $\frac{88.5\times120}{180\times15}=\frac{88.5\times2}{3\times15}=\frac{177}{45}=3.933...$. Then 5.9 - 3.933 = 1.966..., so approximately 1.97, but maybe the problem expects using the same 88.5 for 120 - lb? No, that's wrong. Wait, maybe the original problem is that the 120 - lb person's rate is calculated as (88.5 / 15)(120/180) = 5.9(2/3) ≈ 3.93. Then the difference is 5.9 - 3.93 = 1.97, which is approximately 2.0, but let's check:

Wait, 88.5 calories in 15 minutes for 180 - lb. So per minute: 5.9. For 120 - lb, the rate is (120/180)5.9 = (2/3)5.9 ≈ 3.933. Then 5.9 - 3.933 = 1.966..., so about 1.97, but maybe the problem wants it as 1.97 or 2.0. But let's do exact: 88.5/15 = 5.9. 120/180 = 2/3. 5.9(2/3) = (59/10)(2/3) = 118/30 = 59/15 ≈ 3.933. Then 5.9 - 59/15 = (88.5 - 59)/15 = 29.5/15 ≈ 1.966..., so approximately 1.97. But maybe the problem has a different approach. Wait, maybe the user made a mistake in the problem statement, but assuming that we need to find how much less 120 - lb burns, but the problem says "more" – maybe it's a mistake, and it should be "less", but we'll proceed with the calculation.

Answer:

The 180 - lb person has a higher rate. But for the blank: A 120 - lb person burns \boxed{1.97} (approx) less, but the problem says "more" – maybe a typo. Wait, no, maybe I messed up. Wait, the rate for 180 - lb is 5.9, for 120 - lb: let's calculate the rate correctly. The formula for calories burned in bowling: typically, the number of calories burned per minute is proportional to weight. So if 180 - lb burns 88.5 in 15 min, then 120 - lb burns (120/180)88.5 in 15 min, so per minute: (120/180)5.9 = (2/3)*5.9 ≈ 3.93. Then the difference is 5.9 - 3.93 = 1.97. So the 180 - lb person burns 1.97 more calories per minute than the 120 - lb person. So the blank should be 1.97 (or 2.0 if rounded), and the dropdown is 120 - lb and the other is 180 - lb? Wait, the problem says "A 120 - lb person burns [ ] more calories each minute than a [ ] person" – no, that's incorrect. It should be "A 180 - lb person burns [ ] more calories each minute than a 120 - lb person". So maybe the dropdown is 120 - lb, and the number is 1.97. So the answer for the blank is approximately 1.97 (or 2.0).