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Answers
Step-by-step explanation:
Given:-
1.Five times the length of a ruler increased by 2 inches less than the height of shiela.
2.A dozen of t-shirts added to half a
dozen of shorts has a total cost of not greater than Php. 960.
3.The difference between the number of Php. 100- peso tickets and Php. 50 -peso tickets is not less than 30.
To find:-
Write each statement as a linear in equations in two variables and find the solution.
Solution:-
1.Length of the ruler=r
Height of shiela=s
Five times the length of the ruler increased by 2 inches=5r+2
It is less than height of shiela
=5r+2<s
To get the solution of this in-equation we write it as 5r+2=s
If r=1 then s=5(1)+2=5+2=7
if r=2 then s=5(2)+2=10+2=12
since it is a linear equation it has infinitely many solutions
r=1,2... then s=7,12...
Solution=(1,7),(2,12),...
2.cost of one t-shirt=t
Cost of dozen t-shirts=12t
cost of one short=s
Cost of half dozen short=6s
The sum of dozen t-shirts and half dozen shorts is not greater than Php.960.
=>12t+6s≤960
=>6(2t+s)≤960
=>2t+s≤160
To get solution we write it 2t+s=160
=>s=160-2t
If t=10 then s=160-20=140
if t=20 then s=160-40=120
t=10,20... then s=140,120
Solution=(10,140),(20,120)....
3.Cost of 100-peso tickets=p
Cost of 50-peso tickets=t
the difference between them is not less than 30
=>p-t≥30
We write it for solution p-t=30
=>p=30+t
if p=10=30+10=40
if p=20=30+20=50
p=10,20,.. then 40,50...
Solution =(10,49),(20,50)....
Answer:-
1)5r+s<2
2)2t+s≤160
3)p-t≥30
Used concept:-
Since they are linear equations in two variables they has infinitely many solutions.
Step-by-step explanation:
Given:-
1.Five times the length of a ruler increased by 2 inches less than the height of shiela.
2.A dozen of t-shirts added to half a
dozen of shorts has a total cost of not greater than Php. 960.
3.The difference between the number of Php. 100- peso tickets and Php. 50 -peso tickets is not less than 30.
To find:-
Write each statement as a linear in equations in two variables and find the solution.
Solution:-
1.Length of the ruler=r
Height of shiela=s
Five times the length of the ruler increased by 2 inches=5r+2
It is less than height of shiela
=5r+2<s
To get the solution of this in-equation we write it as 5r+2=s
If r=1 then s=5(1)+2=5+2=7
if r=2 then s=5(2)+2=10+2=12
since it is a linear equation it has infinitely many solutions
r=1,2... then s=7,12...
Solution=(1,7),(2,12),...
2.cost of one t-shirt=t
Cost of dozen t-shirts=12t
cost of one short=s
Cost of half dozen short=6s
The sum of dozen t-shirts and half dozen shorts is not greater than Php.960.
=>12t+6s≤960
=>6(2t+s)≤960
=>2t+s≤160
To get solution we write it 2t+s=160
=>s=160-2t
If t=10 then s=160-20=140
if t=20 then s=160-40=120
t=10,20... then s=140,120
Solution=(10,140),(20,120)....
3.Cost of 100-peso tickets=p
Cost of 50-peso tickets=t
the difference between them is not less than 30
=>p-t≥30
We write it for solution p-t=30
=>p=30+t
if p=10=30+10=40
if p=20=30+20=50
p=10,20,.. then 40,50...
Solution =(10,49),(20,50)....
Answer:-
1)5r+s<2
2)2t+s≤160
3)p-t≥30
Used concept:-
Since they are linear equations in two variables they has infinitely many solutions.