Learn to use variables and write algebraic expressions using garden planning scenarios!
Scenario: You're planning a vegetable garden. You want to plant tomatoes, carrots, and lettuce. Each tomato plant costs $3, each carrot seed packet costs $2, and each lettuce plant costs $1.50. How can we write an expression to find the total cost?
A variable is a letter or symbol that represents an unknown number or quantity. Think of it as a "mystery number" that we need to find or work with.
Let t = number of tomato plants
Let c = number of carrot packets
Let l = number of lettuce plants
We often use letters like x, y, z, or letters that relate to the problem (like t for tomatoes)
Variables help us write general rules that work for any number, not just specific examples
From our garden scenario, we know the costs:
Tomato plants: $3 each
Carrot packets: $2 each
Lettuce plants: $1.50 each
Now let's write an algebraic expression for the total cost:
Total Cost = 3t + 2c + 1.5l
Where t, c, l are the variables
Cost of tomatoes: 3 × t = 3t
$3 times number of tomato plants
Cost of carrots: 2 × c = 2c
$2 times number of carrot packets
Cost of lettuce: 1.5 × l = 1.5l
$1.50 times number of lettuce plants
Let's say you want to buy 4 tomato plants, 3 carrot packets, and 6 lettuce plants. What's the total cost?
Given: t = 4, c = 3, l = 6
Substitute the values
Total Cost = 3(4) + 2(3) + 1.5(6)
Replace variables with numbers
= 12 + 6 + 9 = $27
Calculate step by step
Answer: The total cost for your garden plants is $27!
You're buying school supplies. Pencils cost $0.50 each, notebooks cost $2 each, and erasers cost $0.25 each. Write an expression for the total cost if you buy p pencils, n notebooks, and e erasers.
Total Cost = 0.5p + 2n + 0.25e
Answer
Using the expression from Problem 1, find the total cost if you buy 8 pencils, 3 notebooks, and 4 erasers.
Total Cost = 0.5(8) + 2(3) + 0.25(4)
= 4 + 6 + 1 = $11
Answer: Total cost = $11