SOLUTION: Please help me solve this equation:
numeric word problem using 3 equations.
The sum of three number is 105. The third is 11 less than 10 times the second. Twice the first
Algebra.Com
Question 168836This question is from textbook Prentice Hall Algebra 2 with Trigonometry
: Please help me solve this equation:
numeric word problem using 3 equations.
The sum of three number is 105. The third is 11 less than 10 times the second. Twice the first is 7 more than three times the second. Find the Numbers
This question is from textbook Prentice Hall Algebra 2 with Trigonometry
Found 2 solutions by Mathtut, gonzo:
Answer by Mathtut(3670) (Show Source): You can put this solution on YOUR website!
lets call the numbers a,b,and c
a+b+c=105....eq 1
c=10b-11.....eq 2
2a=3b+7......eq 3
:
lets solve for a in eq 3. a=(3b+7)/2
:
now lets take c's value from eq 2 and a's value from eq 3 and plug them into eq 1
:
((3b+7)/2)+b+(10b-11)=105 multiply all terms by 2
:
3b+7+2b+20b-22=210---> now combine like terms
:
25b=225:
a,b,c........17,9,79 respectively
Answer by gonzo(654) (Show Source): You can put this solution on YOUR website!
let a = first number.
let b = second number.
let c = third number.
-----
sum of 3 numbers is 105
a + b + c = 105
-----
third number is 11 less than 10 times the second.
c = 10*b - 11
-----
twice the first number is 7 more than 3 times the second.
2*a = 3*b + 7
a = (3*b+7)/2
-----
start with:
a + b + c = 105
substitute for a:
(3*b+7)/2 + b + c = 105
substitute for c:"
(3*b+7)/2 + b + 10*b - 11 = 105
-----
equation is now in terms of b and can be solved.
expand all terms by removing parentheses:
3*b/2 + 7/2 + b + 10*b - 11 = 105
multiply both sides of equation by 2:
3*b + 7 + 2*b + 20*b - 22 = 210
combine like terms:
25*b - 15 = 210
add 15 to both sides of equation:
25*b = 225
divide both sides of equation by 25:
b = 9
-----
if b = 9, then:
(3*b+7)/2 = (27+7)/2 = 34/2 = 17 = a
and:
10*b - 11 = 90 - 11 = 79 = c
-----
you have:
a = 17
b = 9
c = 79
total = 105
-----
total = a + b + c = 79 + 9 + 17 = 88 + 17 = 105 (ok)
-----
c = 10*b - 11 becomes:
c = 10*9 - 11 = 90 - 11 = 79 (ok)
-----
a = (3*b+7)/2 becomes:
a = (3*9+7)/2 = (27+7)/2 = 35/2 = 17 (ok)
-----
RELATED QUESTIONS
Please help me solve this word problem:
Find three consecutive even integers such that
(answered by ewatrrr)
Please help me find the equation to this word problem:
{the sum of three numbers is 40. (answered by ewatrrr)
Hello, I've been struggling with forming equations from word problems. I love math but... (answered by josmiceli,satyareddy22)
This word problem is stumping me. I can't figure out how to write the equations needed... (answered by longjonsilver)
Can you teach me how to solve this problem.
The sum of three numbers is 105. The third... (answered by stanbon)
I need help on this word problem. The sum of three numbers is 18 the first is eight times (answered by ankor@dixie-net.com)
Please help me solve the following word problem I'm stuck :
The sum of three numbers... (answered by lwsshak3)
Please help me solve this word problem: The sum of the digits of a two-digit number is... (answered by Theo)
please help me solve this word problem, Find three consecutive integers such that twice... (answered by stanbon)