Systems of equations word problems example 3 | Algebra I | Khan Academy

TL;DR

Zoey deposited nickels and quarters in an electronic piggy bank and the display read $2.00 with 16 coins. Find the number of nickels and quarters.

Transcript

As a birthday gift, Zoey gave her niece an electronic piggy bank that displays the total amount of money in the bank as well as the total number of coins. After depositing some number of nickels and quarters only-- so we only have nickels and quarters-- the display read money $2.00, number of coins 16 How many nickels and quarters did Zoey put in t... Read More

Key Insights

• 🔑 The word problem involves solving a system of equations with two unknowns.
• 😫 The number of nickels and quarters can be determined by setting up equations based on the given information.
• 😀 By rearranging the equations and substituting variables, we can find the values of n and q.
• 🌓 In this specific case, Zoey deposited 10 nickels and 6 quarters.
• 🤑 The total amount of money deposited was $2.00.
• 🪙 The total number of coins deposited was 16.

Questions & Answers

Q: What variables are defined in this word problem?

In this word problem, n represents the number of nickels and q represents the number of quarters.

Q: How do we calculate the total number of coins Zoey deposited?

The total number of coins is the sum of the number of nickels and the number of quarters, which is 16 coins.

Q: How do we calculate the total amount of money Zoey deposited?

The total amount of money is calculated by multiplying the number of nickels by $0.05 and the number of quarters by $0.25, which should equal $2.00.

Q: How can we solve for the number of nickels and quarters?

By substituting the value of q (16 - n) from the first constraint into the second constraint equation, we can solve for n. Solving these equations will give us the values of n and q.

Summary & Key Takeaways

• Zoey gave her niece an electronic piggy bank as a birthday gift.

• The piggy bank displays the total amount of money and the total number of coins.

• After depositing nickels and quarters, the display showed $2.00 with 16 coins.