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One number is four times grater than another number. The sum of the numbers is 78. What are the two numbers?

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2 Answers

Hi Jessica;
I am always happppppppy to helpppppp!
FIRST NUMBER...x
SECOND NUMBER...x+4x
 
(x)+(x+4x)=78
x+x+4x=78
6x=78
Let's divide both sides by 6...
(6x)/6=78/6
x=13
 
x+4x
13+4(13)=13+52=65
 
13+65=78

Comments

Four times greater means four times as great.
I understand what you are saying, but the two interpretations are not grammatically consistent.
 
four times as great=4x
four times greater=x+4x
Let the the first number be  x
and the second number be  y
 
y is 4 times greater than x,   y=4x
 
the sum is 78,   x+y=78
 
Substitute....   x+4x = 78
add the x's...   5x = 78
divide by 5...    x = 78/5
then ...            x = 15.6
and ...  y=4x... y = 62.4
 
solution:  x = 15.6, y = 62.4
 
Alternatively, you can change them to proper fractions:
 
x = 78/5 = 15 3/5
y = 312/5 = 62 2/5
 
 

Comments

Hi John;
I understand your answer.
However, I think four times grater than another number means x+4x, not 4x.
I agree with Vivian. Four times greater than is the same as five times as much.
 
If my salary is 1/2 that of my next door neighbor, than his salary is twice of mine. His salary is not two times greater than mine, because than it would be three times as much.
 
If you are having trouble with this interpretation, consider one person to have a salary of 10,000 per month while another employee of the same company has a salary of 11,000 per month. You would not say that the higher salary was 1.1 times greater than the lower salary, but only 10% greater (or 1.1 times as much).