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Linear Equations Word Problems
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Linear Equations Word Problems
For each problem, define the variable if needed, write a linear equation, and solve. Show your working where requested.
Forming Equations
1.Keira has $92 to spend at a market. She buys 4 identical items costing $p each and has $28 left. Which equation represents the situation?
- 92 − 4p = 28
- 92 + 4p = 28
- 4p − 92 = 28
- 92 − p = 28
2.A batch of muffins uses 840 g of flour to make 12 muffins. If each muffin uses f grams, which equation represents the total flour used?
- 12f = 840
- f + 12 = 840
- 840f = 12
- f − 12 = 840
3.A cyclist travels at a constant speed of 18 km/h for h hours and covers 63 km. Which equation could be used to find h?
- 18 + h = 63
- 18h = 63
- 18 − h = 63
- h ÷ 18 = 63
Solve and Explain
4.Wiremu has $145 for art supplies. He buys 6 sketchbooks at $s each and has $43 left. Write an equation for the situation, then solve to find the cost of one sketchbook. Show your working.
5.A soup recipe uses 750 g of vegetables to make 5 servings. Assume the amount of vegetables is directly proportional to the number of servings. Let x be the grams needed for 9 servings. Write an equation and calculate x.
6.A ferry travels at a steady 72 km/h for 3.5 hours. Let d be the distance travelled in kilometres. Write an equation and calculate d.
Real-World Applications
7.Ari is saving for a kayak costing $465. He has already saved $105 and puts aside $24 each week. Write and solve an equation to find how many weeks it will take him to reach the cost. Explain what the solution means.
8.A monthly data plan costs $18, plus $0.25 for each gigabyte used beyond the included allowance. If a customer's bill is $31, let g be the number of extra gigabytes. Form an equation, solve for g, and check your result.
9.A community hall charges a fixed booking fee of $40 plus $15 per hour. The total charge for a booking was $145. Let h be the number of hours booked. Write an equation and solve to find h.
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