The sun of two numbers is 18. The difference between three times the smaller number and the larger number is 10.
A. Define variables and formulate a system of equations from this
Situation
B. What is the larger number?
A. Define variables and formulate a system of equations from this
Situation
B. What is the larger number?
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Solution:
Given:
L= Large Number
S=Small Number
L+S=18
3*S-L=10
Solve for L on the first equation
L=18-S => Plug this answer into the second equation
3*S-(18-S)=10 => Distribute the -1 sign out
3S-18+S=10 =>Combine the S's
4S-18=10 => add 18 to both sides
4S=28 => divide by 4 both sides
S=7 => plug back into first equation L+S=18
L+7=18 => subtract 7 on both sides
L=11.
Solution
S=7
L=11
Quick check
3*7-11
21-11=10 => which is what we were given to start with so we did it correct.
Given:
L= Large Number
S=Small Number
L+S=18
3*S-L=10
Solve for L on the first equation
L=18-S => Plug this answer into the second equation
3*S-(18-S)=10 => Distribute the -1 sign out
3S-18+S=10 =>Combine the S's
4S-18=10 => add 18 to both sides
4S=28 => divide by 4 both sides
S=7 => plug back into first equation L+S=18
L+7=18 => subtract 7 on both sides
L=11.
Solution
S=7
L=11
Quick check
3*7-11
21-11=10 => which is what we were given to start with so we did it correct.
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18 and a half