A whale swims 200 miles in 5 days. Identify which equation could be used to find how many miles it swims in 16 days.
A. 200=16x
B. y=200×16×5
C. y=40×16
D. y=200×16
C. y=40×16
The correct equation that could be used to find how many miles the whale swims in 16 days is:
D. y = 200 × 16
Option A, 200 = 16x, does not include the factor of 200 which represents the distance the whale swims in 5 days.
Option B, y = 200 × 16 × 5, includes the factor of 200 but also multiplies it by 5, which does not correspond to the number of days.
Option C, y = 40 × 16, does not include the actual distance the whale swims (200 miles) in the equation.
To find the equation that can be used to determine the number of miles a whale swims in 16 days, we can use the concept of proportions.
The whale swims 200 miles in 5 days, so we can set up a proportion using the miles (y) and the number of days (x):
200 miles / 5 days = y miles / 16 days
To find the equation, we need to solve for y. Cross-multiplying gives us:
5 (y miles) = 200 miles × 16 days
Combining the terms, we have:
5y = 3200
To isolate y, we divide both sides of the equation by 5:
y = 3200 / 5
Now we can simplify:
y = 640
Therefore, the equation that can be used to find the number of miles the whale swims in 16 days is:
y = 640
Looking at the options provided:
A. 200 = 16x does not take into account the proportional relationship between days and the number of miles swam.
B. y = 200 × 16 × 5 is incorrect as it includes the unnecessary multiplication of 5.
C. y = 40 × 16 does not consider the original distance of the whale at 200 miles.
D. y = 200 × 16 is the correct equation that represents the proportional relationship between miles swam and days. The whale swims 200 miles in 16 days.
Therefore, the correct equation is D. y = 200 × 16.