Answer:
The consecutive numbers are 62 and 63
Step-by-step explanation:
Let the larger number be represented by x and the smaller number by y,
Provided they are consecutive numbers;
[tex]x = y + 1[/tex] --- Equation 1
From the question; we have that
[tex]\frac{4x}{7} = \frac{y}{2} + 5[/tex] --- Equation 2
Required
Find x and y
Multiply both sides of equation 2 by 14
[tex]14 * \frac{4x}{7} = 14 * \frac{y}{2} + 14 * 5[/tex]
[tex]2 * 4x = 7 * y + 70[/tex]
[tex]8x = 7y + 70[/tex] ---- Equation 3
Substitute y + 1 for x in equation 2
[tex]8(y + 1) = 7y + 70[/tex]
Open bracket
[tex]8y + 8 = 7y + 70[/tex]
Collect like terms
[tex]8y - 7y = 70 - 8[/tex]
[tex]y = 62[/tex]
[tex]x = y + 1[/tex]
So,
[tex]x = 62 + 1[/tex]
[tex]x = 63[/tex]
Hence, the consecutive numbers are 62 and 63
