Verbal Problems
VERBAL PROBLEMS
A. NUMBER RELATIONSHIP
1. One number is 5 times another number. Their sum is 48. Find the numbers.
Solution:
Let x be the first number
5x be the second number
x+5x=48
6x=48
x=8
5x=5(8)
=40
The first number is 8 and 5 times 8 is 40. Hence, the sum is 48. Hence, the 1st number is 8 and the second number is 40.
2. The product of two consecutive positive numbers is 72. What are the numbers?
Solution:
Let x be the smaller number
x+1 be the next number
(x)(x+1)=72
x2+x-72=0
(x+9)(x+8)=0
x+9= 0 or x-8=0
x=-9 or x=8
reject x=-9 since the number must be positive.
X=8 the smaller number.
X+9= the next number
The smaller number is 8 and the next is 9, hence their product is 72.
3. Four times the square of an integer less 10 times the integer gives 50. Find the number.
Solution:
Let n be the number
4(n)2-10(n)=50
4n2-10n-50=0 divide both sides by 2
2n2-5n-25= 0
(2n+5)(n-5)=0
2n+5=0 or n-5=0
2n/2=-5/2 or n=5
n= -5/2 reject this since it is not an integer, thus the required number is 5.