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Answer:

We can express numbers in its expanded form.

• 2 = 2×1
• 45 = 5×1 + 4×10
• 344 = 4×1 + 4×10 + 3×100

Now, assume a number XY.

The number is expressed as 10X+Y.

Now,

A certain number of two digits is equal to five times the sum of the digits. So,

[tex]\to \sf 10X + Y = 5(X + Y)[/tex]

[tex]\to \sf 10X + Y = 5X + 5Y[/tex]

[tex]\to \sf 5X = 4Y[/tex]

[tex]\to \sf \dfrac{5}{4} X = Y \: --(1)[/tex]

Three times the larger digit exceeds three times the smaller by three.

The larger digit is y according to eq(1).

[tex]\to \sf 3Y - 3X = 3[/tex]

[tex]\to \sf Y - X = 1 \: --(2)[/tex]

Substitute Eq(1) in Eq(2).

[tex]\to \sf \dfrac{5}{4} X - X = 1[/tex]

[tex]\to \bf X = 4[/tex]

Substitute x = 4 in eq(1). we get:

[tex]\to \bf Y = 5[/tex]

Therefore, the number is 10X+Y:

[tex]\to \sf 10X+Y[/tex]

[tex]\to \sf 10(4) + 5[/tex]

[tex]\bigstar \bf 45[/tex]

Therefore, the required number is 45.