Question 1 : Kim's age is four times that of her sister. When you add Kim's age to her sister's age, you get 60. How old is each sister?
Write an equation that represents the situation. Explain any variable used.
Solve the equation from Part (a). Show your work. State your solution as a complete sentence.
Answer:
Showing\: ages\:using\:two\:variables
Let age of kim's sister be x years
And, age of Kim be y years
In question, it is given that the age of Kim is 4 times of her sister's age, so
Kim's age = 4 × her sister's age
= > y = 4 × x
= > y = 4x -----: ( 1 )
Given, if we add the ages of Kim and his sister is 60 years
= > age of Kim + age of kim's sister = 60
= > x + y = 60
Putting the value of y from ( i ) ,
= > x + 4x = 60
Hence, \: equation \:representing\: the\: situation\: is\: ( x + y = 60 ) \:or \:( x + 4x = 60 )
Solving equation :
= > x + 4x = 60
= > 5x = 60
= > 5 × x = 5 × 12
= > x = 12
Hence,
Age of Kim's sister = x years = 12 years Age of Kim = y years = 4x years = 4( 12 years ) = 48 years
For verification ,
Age of kim's sister + age of Kim = 60
RHS => x + y => 12 + 48 => 60
LHS => 60
RHS = LHS
Hence, ages are correct.
Question 2 : Solve each given equation and show your work. Tell whether it has one solution, an infinite number of solutions, or no solutions.
( a ) : 6x + 4x - 6 = 24 + 9x
( b ) : 25 - 4x = 15 - 3x + 10 - x
( c ) : 4x + 8 = 2x + 7 + 2x - 20
Answer :
( a ) :
= > 6x + 4x - 6 = 24 + 9x
= > 10x - 6 = 24 + 9x
= > 10x - 6 + 6 - 9x = 24 + 9x + 6 - 9x
= > x = 30
Hence, a has one solution .
( b ) :
= > 25 - 4x = 15 - 3x + 10 - x
= > 25 - 4x = 15 + 10 - 3x - x
= > 25 - 4x = 25 - 4x
As left hand side and right hand side are equal to each other. Equation has infinitely many solutions.
( c ) :
= > 4x + 8 = 2x + 7 + 2x - 20
= > 4x + 8 = 2x + 2x + 7 - 20
= > 4x + 8 = 4x - 13
= > 8 = - 13
According to the equation, 8 is equal to - 13 but it is not, so given equation has no solution.
Question 3 : At a bargain store, Tanya bought 4 items that each cost the same amount. Tony bought 5 items that each cost the same amount, but each was $1.25 less than the items that Tanya bought. Both Tanya and Tony paid the same amount of money. What was the individual cost of each person's items? Write an equation. Let x represent the cost of one of Tanya's items. Solve the equation. Show your work. Check your solution. Show your work. State the solution in complete sentences.
Let cost of one item of tanya be x , Given, tanya bought 4 times ,
So, total money paid by tanya = 4 × x = 4x
Tony bought 5 items at y , Tony bought 5 cm items
So, total money = 5 × y = 5y
Given that amount of each amount bought by Tony was $1.25 lesser than the cost of items of tanya,
Amount of one item of tanya - 1.25 = amount of one item of Tony
= > x - 1.25 = y
= > x = y + 1.25 ----: ( 1 )
Given that they paid the same amount, so
Amount paid by tanya = amount paid by Tony
= > 4x = 5y
Putting the value of x from ( 1 ) ,
= > 4( y + 1.25 ) = 5y
= > 4y + 5 = 5y
= > 5 = 5y - 4y
= > 5 = y
Putting the value of y in ( 1 ),
x = y + 1.25
= > x = 5 + 1.25
= > x = 6.25
Hence, cost of each item bought by tanya = $ 6.25 Cost of each item bought by Tony = $ 5
Checking the solution :
If our solution is correct,
= > total Amount paid by tanya = total amount paid by Tony
= > 4( 6.25 ) = 5( 5 )
= > 25 = 25
LHS =RHS
Hence, our solution is correct.
3 votes Thanks 37
abhi569
Aise kuch aur bhi hai.... Lekin unki link nhii
Answers & Comments
Verified answer
Question 1 : Kim's age is four times that of her sister. When you add Kim's age to her sister's age, you get 60. How old is each sister?Write an equation that represents the situation. Explain any variable used.
Solve the equation from Part (a). Show your work. State your solution as a complete sentence.
Let age of kim's sister be x years
And, age of Kim be y years
In question, it is given that the age of Kim is 4 times of her sister's age, so
Kim's age = 4 × her sister's age
= > y = 4 × x
= > y = 4x -----: ( 1 )
Given, if we add the ages of Kim and his sister is 60 years
= > age of Kim + age of kim's sister = 60
= > x + y = 60
Putting the value of y from ( i ) ,
= > x + 4x = 60
Solving equation :
= > x + 4x = 60
= > 5x = 60
= > 5 × x = 5 × 12
= > x = 12
Hence,
Age of Kim's sister = x years = 12 years
Age of Kim = y years = 4x years = 4( 12 years ) = 48 years
For verification ,
Age of kim's sister + age of Kim = 60
RHS => x + y => 12 + 48 => 60
LHS => 60
RHS = LHS
Hence, ages are correct.
Question 2 : Solve each given equation and show your work. Tell whether it has one solution, an infinite number of solutions, or no solutions.
( a ) : 6x + 4x - 6 = 24 + 9x
( b ) : 25 - 4x = 15 - 3x + 10 - x
( c ) : 4x + 8 = 2x + 7 + 2x - 20
( a ) :
= > 6x + 4x - 6 = 24 + 9x
= > 10x - 6 = 24 + 9x
= > 10x - 6 + 6 - 9x = 24 + 9x + 6 - 9x
= > x = 30
Hence, a has one solution .
( b ) :
= > 25 - 4x = 15 - 3x + 10 - x
= > 25 - 4x = 15 + 10 - 3x - x
= > 25 - 4x = 25 - 4x
As left hand side and right hand side are equal to each other.
Equation has infinitely many solutions.
( c ) :
= > 4x + 8 = 2x + 7 + 2x - 20
= > 4x + 8 = 2x + 2x + 7 - 20
= > 4x + 8 = 4x - 13
= > 8 = - 13
According to the equation, 8 is equal to - 13 but it is not, so given equation has no solution.
Question 3 : At a bargain store, Tanya bought 4 items that each cost the same amount. Tony bought 5 items that each cost the same amount, but each was $1.25 less than the items that Tanya bought. Both Tanya and Tony paid the same amount of money. What was the individual cost of each person's items? Write an equation. Let x represent the cost of one of Tanya's items.
Solve the equation. Show your work.
Check your solution. Show your work.
State the solution in complete sentences.
Let cost of one item of tanya be x ,
Given, tanya bought 4 times ,
So, total money paid by tanya = 4 × x = 4x
Tony bought 5 items at y ,
Tony bought 5 cm items
So, total money = 5 × y = 5y
Given that amount of each amount bought by Tony was $1.25 lesser than the cost of items of tanya,
Amount of one item of tanya - 1.25 = amount of one item of Tony
= > x - 1.25 = y
= > x = y + 1.25 ----: ( 1 )
Given that they paid the same amount, so
Amount paid by tanya = amount paid by Tony
= > 4x = 5y
Putting the value of x from ( 1 ) ,
= > 4( y + 1.25 ) = 5y
= > 4y + 5 = 5y
= > 5 = 5y - 4y
= > 5 = y
Putting the value of y in ( 1 ),
x = y + 1.25
= > x = 5 + 1.25
= > x = 6.25
Hence,
cost of each item bought by tanya = $ 6.25
Cost of each item bought by Tony = $ 5
Checking the solution :
If our solution is correct,
= > total Amount paid by tanya = total amount paid by Tony
= > 4( 6.25 ) = 5( 5 )
= > 25 = 25
LHS =RHS
Hence, our solution is correct.