3 roads, a, b, and

1 answer:

7 0

3 roads...a, b and c

b = 3a.....a = 1/3b
c = 2b.....b = 1/2c.....

a ------|
b ------|--------|------|
c ------|--------|------|------|------|------|

so a is 1/6 of the total road <===

if road b is 7 miles longer the a...
b = 3a....b = a + 7
a + 7 = 3a
7 = 3a - a
7 = 2a
7/2 = a
3.5 = a

b = 3a
b = 3(3.5)
b = 10.5

c = 2b
c = 2(10.5)
c = 21 <=====road C is 21

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If X and Y are distinct digits such that the eight-digit number 7448X24Y is divisible by both 8 and 9, then find X - Y.

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<h3>How to determine the distinct digits X and Y?</h3>

The eight-digit number is given as:

7448X24Y

Also, from the question

The number is divisible by 8 and 9

When a number is divisible by 8, then the last three digits of that number would be divisible by 8.

When a number is divisible by 9, the sum of the digits of the number would be divisible by 9.

So, we have:

24Y is divisible by 8

The possible value of Y from the above statement is 0

This is so because 240 is divisible by 8

The sum of the digits of the number would be divisible by 9.

This means that:

7 + 4 + 4 + 8 + X + 2 + 4 + Y = 29 + X + Y

Substitute 0 for Y

29 + X + Y = 29 + X + 0

Evaluate the sum

29 + X + Y = 29 + X

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So, we have

29 + X = 36

Subtract 29 from both sides of the equation

X = 7

So, we have

X = 7 and Y = 0

X - Y is calculated as:

X - Y = 7 - 0

Evaluate the difference in the above equation

X - Y = 7

Hence, the value of X - Y such that the eight-digit number 7448X24Y is divisible by both 8 and 9 is 7

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