Question

the sum of two numbers is 54. if the smallest number is 6 less than the bigger one, find the number

Answer 1

Answer:

x + y = 54…Eq…1

+ y = 54…Eq…1and their difference is nine more than the smaller number.

+ y = 54…Eq…1and their difference is nine more than the smaller number.x - y = y + 9

+ y = 54…Eq…1and their difference is nine more than the smaller number.x - y = y + 9x - y - y = 9

+ y = 54…Eq…1and their difference is nine more than the smaller number.x - y = y + 9x - y - y = 9x - 2y = 9

+ y = 54…Eq…1and their difference is nine more than the smaller number.x - y = y + 9x - y - y = 9x - 2y = 9x = 9 + 2y…Eq.2

+ y = 54…Eq…1and their difference is nine more than the smaller number.x - y = y + 9x - y - y = 9x - 2y = 9x = 9 + 2y…Eq.2Now substituting the value of x from Eq..2 to Eq..1

+ y = 54…Eq…1and their difference is nine more than the smaller number.x - y = y + 9x - y - y = 9x - 2y = 9x = 9 + 2y…Eq.2Now substituting the value of x from Eq..2 to Eq..1x + y = 54

+ y = 54…Eq…1and their difference is nine more than the smaller number.x - y = y + 9x - y - y = 9x - 2y = 9x = 9 + 2y…Eq.2Now substituting the value of x from Eq..2 to Eq..1x + y = 549 + 2y + y = 54

9 + 3y = 54

9 + 3y = 543y = 54 - 9

9 + 3y = 543y = 54 - 93y = 45

9 + 3y = 543y = 54 - 93y = 45y =45/3

9 + 3y = 543y = 54 - 93y = 45y =45/3y = 15

9 + 3y = 543y = 54 - 93y = 45y =45/3y = 15The smaller number is 15

9 + 3y = 543y = 54 - 93y = 45y =45/3y = 15The smaller number is 15Now substituting the value of y in Eq..2

9 + 3y = 543y = 54 - 93y = 45y =45/3y = 15The smaller number is 15Now substituting the value of y in Eq..2x = 9 + 2y

9 + 3y = 543y = 54 - 93y = 45y =45/3y = 15The smaller number is 15Now substituting the value of y in Eq..2x = 9 + 2yx = 9 + 2×15

9 + 3y = 543y = 54 - 93y = 45y =45/3y = 15The smaller number is 15Now substituting the value of y in Eq..2x = 9 + 2yx = 9 + 2×15x = 9 + 30

9 + 3y = 543y = 54 - 93y = 45y =45/3y = 15The smaller number is 15Now substituting the value of y in Eq..2x = 9 + 2yx = 9 + 2×15x = 9 + 30x = 39

Answer the two numbers, larger is 39 and smaller is 15.

Now check the correctness of answer by taking their sum, which should be 54 as per statement

Now check the correctness of answer by taking their sum, which should be 54 as per statementx + y = 54

Now check the correctness of answer by taking their sum, which should be 54 as per statementx + y = 5439 + 15 = 54

Now check the correctness of answer by taking their sum, which should be 54 as per statementx + y = 5439 + 15 = 5454 = 54