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Algebraic Expressions and Equations

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  • A taxi charges €5 flat fee and then €2 per km. Write an algebraic expression and find the total cost if Joe travels for 5km.
    2x + 5, €15
  • Albert thinks of a number, doubles it and removes 7. He then multiplies the answer by 8. Write a simplified expression.
    8 (2x - 7) = 16x - 56
  • The formula for changing km to miles is m = 5k / 8. Calculate 40km in miles.
    25 miles
  • A company spends 3x + 2x + 5y − y euros on transport and supplies. Write a simplified expression.
    5x + 4y
  • If the cost of a child’s ticket is €x and an adult’s ticket is €y, write an algebraic expression to represent the total cost for 3 children and 2 adults.
    3x + 2y
  • A phone company charges a base fee of €5 and then 25c per SMS. Roy's bill was €12.50. How many SMS did he send?
    30
  • The price of buying x chairs and y tables is 50x + 100y. Find the cost of buying 6 chairs and 2 tables.
    500
  • In a game, x tokens are won per level and y tokens are deducted per penalty. Write an algebraic expression for the number of tokens after 5 levels with 2 penalties.
    5x - 2y
  • In a game, Sue obtained the following tokens: 3a, 2b, 4a, and b. Write a simplified expression for the number of tokens.
    7a + 3b
  • A car drives (2x + 6) km per hour. Find the total distance driven in 6 hours.
    6 (2x+6) = 12x + 36
  • A garden has width x and length y. Formulate an expression for the perimeter of the garden and use it to calculate the perimiter when the width is 3m and the length is 2m.
    2x + 2y, 10m
  • Karen gave her cat c grams of dry food every day for 30 days until the packet was finished. If the packet contains 2.7kg, how many grams did Karen give every day? Write an algebraic equation and solve it.
    90 grams
  • Mary ordered x photos each costing €0.20 and she had to pay an extra €5 for delivery. If the total cost was €12, how many photos did she order? Write an algebraic equation and solve it.
    35 photos
  • Write and expand an algebraic expression to find the cost of 3 packs of pens, where each pack costs €x, and a discount of €4 is applied to each pack.
    3(x - 4) = 3x - 12
  • A shop is keeping a record on the amount of shirts and pants sold during the weekend. On Friday 5 shirts and 2 pants were sold, on Saturday 6 shirts and 3 pants were sold but 2 pants were returned. Write a simplified algebraic expression.
    5s + 2p + 6s + 3p - 2p = 11s + 3p
  • Write an algebraic expression to find the cost of a bill after a discount of €50.
    b - 50
  • A bus costs €120 to rent for a day. Write an algebraic expression to find the cost per person if n people are on the bus.
    120/n