SOLUTION: The sum of two numbers is 40. If twice the larger number is divided by the smaller, the quotient is 3 and the reminder is 10. Find the number. I NEED HELP. PLEASE!!!! The answer is
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Question 121866This question is from textbook Algebra: structure and method: Book 1
: The sum of two numbers is 40. If twice the larger number is divided by the smaller, the quotient is 3 and the reminder is 10. Find the number. I NEED HELP. PLEASE!!!! The answer is 26 or 14, but I do not know how to get there.
This question is from textbook Algebra: structure and method: Book 1
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
We will go thru this step-by-step
Let x = the larger number
Let y = the smaller number
:
Write an equation for each statement
"The sum of two numbers is 40."
x + y = 40
or we can say:
x = (40-y); use for substitution
:
" If twice the larger number is divided by the smaller, the quotient is 3 and the reminder is 10."
:
If we think about long division, we can say that if we subtract 10 from 2x and
divide by y, the quotient will be an even 3, write the equation like that;
= 3
multiply both sides by y
2x - 10 = 3y
2x = 3y + 10
:
Find the number.
:
Substitute (40-y) for x in the above equation and find y
2(40-y) = 3y + 10
80 - 2y = 3y + 10
80 - 10 = 3y + 2y
70 = 5y
y =
y = 14 is the smaller number
:
The larger number (x)
40 - 14 = 26 is the larger number
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