Question

if (5a-1) is divided by b, the result is 3 and the remainder is 4. If (b+8) is divided by a, the result is 3 and the remainder is 1/4a (¼a). Form two equations in a and b. Solve for a and b.​

Answer 1

a = 4

b = 5

Explanation:

We should understand that the product of the result of a division (quotient) and the number divided (divisor) plus the remainder, will give the number we are dividing (dividend)

From the first equation;

5a - 1 = 3(b) + 4

5a - 1 = 3b + 4

5a - 3b = 4 + 1

5a - 3b = 5 •••••(i)

Secondly;

b + 8 = 3(a) + a/4

Multiply through by 4

4b + 32 = 12a + a

4b + 32 = 13a

4b - 13a = -32 ••••••••(ii)

Multiply equation i by 4 and ii by 3

20a -12b = 20

12b -39a = -96

Add both equations

20a-39a = 20-96

-19a = -76

a = 76/19

a = 4

Recall;

5a-3b = 5

5(4) - 3b = 5

20 - 3b = 5

20-5 = 3b

3b = 15

b = 15/3

b = 5