1. A two digit number is three less than seven times the sum of its digits. if the digits are reversed, the new number is 18 less than the original number. what is the new number?

Question

2. The numerator a fraction is 3 less than the denominator. If 5 is added to both the numerator and denominator, the value of the resulting fractin is 3/4. Find the original fraction.

3. The difference between the first and second number is 0. Find the numbers such that the difference between thrice the first and twice the second is 18.

4. A theater show charges 60 for adults and 48 for seniors. On a day when 310 people paid an admission, the total receipts were 18,192. How many who paid were adults? How many were seniors.

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Answer 1

4. Let x = seniors and y = adults

y = 310 - x

60y + 48x = 18,192

Substitute 310-x for y in second equation and solve for x. Insert that value into the first equation and solve for y. Check by inserting both values into the second equation.

Answer 2

1. new number is 35

Let x is digit in 10th place and y be in unit place of original number. and the original number is 10x+y
iven 10x+y=7(x+y)-3
Thus we get 3x-6y=-3 ......(i)
The reverse of original number is 10y+x
Also given 10y+x=10x+y-18,
that is 9x-9y=18 ......(ii)
solving (i) and (ii)get x=5 and y=3.
That is the original number is 53 and new number is 35

Answer 3

2. Let x be the numerator and y be the denominator.
Given x = y - 3
Also (x + 5)/ (y + 5) = 3/4
Substitute x = y - 3 in the above equation we get (y + 2) / (y + 5) = 3/4
Cross multiply this we get y = 7 and substitute y in first equation gives x = 4
Thus the fraction is 4/7