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Year 6 Sats. Test


(Peterborough, England)









































A group of 30 pupils is on a trip.

It costs £5.00, including lunch.

Some children take a pack lunch.

They pay only £3.00.

The 30 children pay total of £110.00.

How many children take their own pack lunch?

Comments for Year 6 Sats. Test

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May 09, 2013
Write Equations, Solve for Unknown
by: Staff


Answer

Part I


Selection of Variables

x = number of children who pay $5 for trip and lunch

y = number of children who pay $3 for trip, but take a pack lunch

Selection of x and y variables




total number of students = 30

Equation x + y = 30 for total number of students





The 30 children pay total of £110.00.

Equation 5x + 3y = 110 for total amount students pay





There are two equations with two unknowns

Two Equations and Two Unknowns

    x + y = 30
 
  5x + 3y = 110





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May 09, 2013
Write Equations, Solve for Unknown
by: Staff

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Part II

solve for x in the first equation

subtract y from each side of the first equation

Solve for x in the first equation:  x + y = 30
 
  subtract y from each side of the first equation




solve for y (the only value requested in the problem statement) by substitution, using the second equation

substitute (30 - y) for x

Solve for y by substitution, using the second equation
 
  substitute (30 - y) for x





By substituting (30 - y) for x, the second equation has been transformed into one equation with one unknown.

Solve for y


Use the distributive law to eliminate the parentheses on the left side of the equation.

Solve for y
 
  Use the distributive law to eliminate the parentheses on the left side of the equation.






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May 09, 2013
Write Equations, Solve for Unknown
by: Staff

--------------------------------------------------------


Part III


Combine like terms.

Simplify Equation
 
  Combine like terms





Add 2y to each side of the equation

Add 2y to each side of the equation





Subtract 110 from each side of the equation

Subtract 110 from each side of the equation





Divide each side of the equation by 2

Divide each side of the equation by 2






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May 09, 2013
Write Equations, Solve for Unknown
by: Staff

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Part IV


Final Answer:

Math - Final Answer:  A group of 30 pupils is on a trip. 
 
It costs £5.00, including lunch. 
 
Some children take a pack lunch. 
 
They pay only £3.00. 
 
The 30 children pay total of £110.00. 
 
<br>How many children take their own pack lunch?






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check the answer using

y = 20

x = 30 - y

x = 30 - 20

x = 10

5x + 3y = 110

substitute 10 for x and 20 for y

5*10 + 3*20 = 110

50 + 60 = 110

110 = 110, OK → x = 10 and y = 20 are valid solutions






Thanks for writing.

Staff
www.solving-math-problems.com


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