A new vintage 1965 convertible requires an oil change every 400

miles and replacement of all fluids every 19,000

miles. If these services have just been performed by the dealer, how many miles from now will both be due at the same time?

The answer is that 38,000 miles from now oil change and fluids replacement be due at the same time.

Step-by-step explanation:

1. Let's review the information given to us to answer the question correctly:

Oil change every 400 miles

Fluids replacement every 19,000 miles

2. If these services have just been performed by the dealer, how many miles from now will both be due at the same time?

For finding the correct answer we should find the least common multiple of 400 and 19,000, this way:

List the prime factors of each.

400 = 2 * 2 * 2 * 2 * 5 * 5

19,000 = 2 * 2 * 2 * 5 * 5 * 5 * 19

Now we multiply each factor the greatest number of times it occurs in either number. 400 has four times 2 and 2 times five 5, and 19,000 has three times 2, 3 times 5 and a 19, so we multiply 2 four times, 5 three times, and 19 once. This gives us 38,000, the smallest number that can be divided by both 400 and 19,000.

The answer is that 38,000 miles from now oil change and fluids replacement be due at the same time.