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Algebra Problem Solving
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Algebra Problem Solving
Solve each problem and show your working. Check that your answers make sense in the original situation.
Algebra in action
Use variables to represent unknown amounts, form equations and solve them using clear steps.
1.At a farmers' market, Bodhi has x apples in a crate. Chloe has three times as many apples as Bodhi. Altogether they have 36 apples. Write and solve an equation to find how many apples Bodhi has.
2.A rectangular produce sign has a length of (3x + 2) cm and a width of (x − 1) cm. Its area is 40 cm². Form an equation using brackets and find the positive value of x, then state the sign's dimensions.
3.Tahnee arranges three consecutive whole-number prices for bunches of herbs. Their total is $72. Let n be the smallest price. Write an equation and find all three prices.
4.A market stall sells a basket for 80% of its original price. The discounted price is $32, and the original price is (x + 8) dollars. Find x and the original price.
5.A box contains x jars of honey. A stallholder adds 4 more boxes, each holding x jars, then adds 7 loose jars. Which expression represents the total number of jars?
- 4(x + 7)
- 5x + 7
- 4x + 7
- 5(x + 7)
6.A customer buys 3 identical bags of pears and pays a $5 bag fee. The total is $29. Write and solve an equation to find the price of one bag of pears.
7.A stallholder simplifies 4(2x − 3) as 8x − 3. Is this correct? Choose the best explanation.
- Yes, because 4 is multiplied only by the first term.
- No, because 4 must multiply both terms; the result is 8x − 12.
- No, because the result is 8x + 12.
- Yes, because brackets do not affect multiplication.
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