un numero supera en 43 a otro. Si el mayor se divide entre el menor, el cociente es 5 y el residuo es 7. Encontrar los numeros.

The smaller number is 9 and the greater number is 52.

Explanation:

1. Name the smaller number x and the greater number y

2. One number is 43 greater than the other:

y - x = 43 [equation 1]

3. If the greater numbrer is divided by the smaller, the quotient is 5 and the remainder is 7:

y = 5x + 7 [equation 2]

4. Substitute y into the equation 1, to find x:

5x + 7 - x = 43 4x = 43 - 7 4x = 36 x = 36 / 4 x = 9

5. Substitute x = 9 into the equation 2, to find y:

y = 5 (9) + 7 = 45 + 7 = 52