Linear Equations: The Delivery Fee Has Entered the Chat
You agree to split a fictional snack delivery with friends. Each snack costs $3, delivery costs $4, and the total is $19. Someone asks how many snacks arrived. Apparently x has been hiding in the takeout bag.
Start here
A variable is a label for a quantity you do not know yet. Let x mean the number of snacks. The total has a fixed part, $4, and a changing part, $3 for every snack. That gives 4 + 3x = 19.
Work backward
Subtract 4 from both sides: 3x = 15. Then divide both sides by 3: x = 5. There were five snacks. Doing the same operation to both sides keeps the statement balanced.
Check the story
Put 5 back into the original equation: 4 + 3 × 5 = 19. The result fits. Also notice that a snack count should be a whole number here. If your answer were 5.7, you would need to check the arithmetic or the assumptions.
Level up: compare two plans
Suppose Plan A charges $4 plus $3 per snack. Plan B charges $10 plus $2 per snack. Set their totals equal: 4 + 3x = 10 + 2x. Subtract 2x and then subtract 4: x = 6. Both cost $22 for six snacks. At seven snacks, A costs $25 and B costs $24.
Try it
A pretend craft kit charges $6 for shipping plus $4 per item. The total is $30. Write an equation and find the number of items. Ignore tax for this example.
Check your answer
6 + 4x = 30. Subtract 6 to get 4x = 24. Divide by 4 to get x = 6 items. Check: 6 + 4 × 6 = 30.
Save this
Name the unknown. Separate fixed cost from cost per item. Write the equation. Undo operations equally on both sides. Check the answer in the original story. Algebra did not disappear; it started charging delivery.
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