Today you will learn to translate written information into ... - Free Printable

You're asked to write a “let” statement for each of the mathematical equations labeled (b), (c), and (d). A “let” statement defines what variable(s) represent in the context of the word problem.

Let’s match each equation to its corresponding word problem and write an appropriate “let” statement.

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🔹 Equation (b):

12z + 5(z + 2) = 30

This matches Problem #3:
> Eddie, who earns $5 per hour, worked two hours longer than Zach, who earns $12 per hour. Together they earned $30.

- Let z = number of hours Zach worked.
- Then z + 2 = number of hours Eddie worked.
- Zach’s earnings: 12 × z = 12z
- Eddie’s earnings: 5 × (z + 2) = 5(z + 2)
- Total: 12z + 5(z + 2) = 30 → matches equation (b)

✔ “Let” statement for (b):
> Let z represent the number of hours Zach worked.

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🔹 Equation (c):

z + (z − 2) + 5(z − 2) = 30

This matches Problem #1:
> A zoo has two fewer elephants than zebras and five times more monkeys than elephants. The total number of elephants, monkeys, and zebras is 30.

Let’s define:
- Let z = number of zebras.
- Then elephants = z − 2 (two fewer than zebras)
- Monkeys = 5 × elephants = 5(z − 2)

Total animals:
zebras + elephants + monkeys = z + (z − 2) + 5(z − 2) = 30 → matches equation (c)

✔ “Let” statement for (c):
> Let z represent the number of zebras in the zoo.

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🔹 Equation (d):

z + 12z = 30

This matches Problem #2:
> Thirty ounces of metal is created by mixing zinc with silver. The number of ounces of silver needed is twelve times the number of ounces of zinc.

Let’s define:
- Let z = number of ounces of zinc.
- Then silver = 12z (twelve times the zinc)
- Total metal: zinc + silver = z + 12z = 30 → matches equation (d)

✔ “Let” statement for (d):
> Let z represent the number of ounces of zinc used.

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## ✔ Final Answers:

b. Let z represent the number of hours Zach worked.
c. Let z represent the number of zebras in the zoo.
d. Let z represent the number of ounces of zinc used.

These “let” statements clearly define the variable z in the context of each real-world problem, which is essential for translating word problems into algebraic equations.