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

 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 total number of students = 30 The 30 children pay total of £110.00. There are two equations with two unknowns --------------------------------------------------------

 May 09, 2013 Write Equations, Solve for Unknown by: Staff --------------------------------------------------------Part IIsolve for x in the first equationsubtract y from each side of the first equationsolve for y (the only value requested in the problem statement) by substitution, using the second equationsubstitute (30 - y) for xBy substituting (30 - y) for x, the second equation has been transformed into one equation with one unknown.Solve for yUse the distributive law to eliminate the parentheses on the left side of the equation. --------------------------------------------------------

 May 09, 2013 Write Equations, Solve for Unknown by: Staff --------------------------------------------------------Part IIICombine like terms.Add 2y to each side of the equationSubtract 110 from each side of the equationDivide each side of the equation by 2 --------------------------------------------------------

 May 09, 2013 Write Equations, Solve for Unknown by: Staff --------------------------------------------------------Part IVFinal Answer:---------------------------------------------------------------check the answer using y = 20x = 30 - yx = 30 - 20x = 105x + 3y = 110substitute 10 for x and 20 for y5*10 + 3*20 = 11050 + 60 = 110110 = 110, OK → x = 10 and y = 20 are valid solutions Thanks for writing.Staff www.solving-math-problems.com

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