Question

The sum of two numbers is 2490.if 65% of one number is equal to 85% of the other, the smallest is?

Answer 1

the smallest number is 1079

Explanation:

Let the numbers be x and y

• We have two equations
  x + y = 2490 (1)
  0.65x = 0.85y (2)
  

• Take the first equation
  
  `x + y = 2490`

• Move y to the right side:
  
  `x=2490-y`
  
• Substitute for x in the second equation:
  
  `0.65x=0.85y`
  
  `0.65\left(2490-y\right)=0.85y`
  
  `1618.5-0.65y=0.85y`
  
• Multiply throughout by 100:
  
  `161850 - 65y = 85y`
  
• Move 161850 to the right side:
  
  `-65y=85y-161850`
  
• Move 85y to the left side:
  
  `-65y=85y-161850`
  
  `-150y=-161850`
  
• Divide both sides by -150
  
  `(-150y)/(-150)=(-161850)/(-150)`
  
  `y=1079`
  
• Substitute for y in x = 2490 -y
  
  `x=2490-1079`
  
  `x=1411`
  
• So the smaller number is 1079 and the larger number is 1411