AI tutor
Welcome to Bytelearn!
Let’s check out your problem:
Ezra and Zoe are playing the new video game Knights of the Dawn. At the start of level , Ezra had two-thirds as many gold coins as Zoe. During the level, Ezra found gold coins, but Zoe only found . At the end of the level, both players had the same number of gold coins.Which equation can you use to find , the number of gold coins Zoe had at the start of level ?Choices:(A) (B) How many gold coins did Zoe have at the start of level ? gold coins
Full solution
Q. Ezra and Zoe are playing the new video game Knights of the Dawn. At the start of level , Ezra had two-thirds as many gold coins as Zoe. During the level, Ezra found gold coins, but Zoe only found . At the end of the level, both players had the same number of gold coins.Which equation can you use to find , the number of gold coins Zoe had at the start of level ?Choices:(A) (B) How many gold coins did Zoe have at the start of level ? gold coins
- Rephrase the Problem: Let's first rephrase the ＂How many gold coins did Zoe have at the start of level in the video game Knights of the Dawn?＂
- Set Up Equation: We need to set up an equation to represent the situation. Let's let represent the number of gold coins Zoe had at the start of level . According to the problem, Ezra had two-thirds as many gold coins as Zoe at the start, so Ezra had gold coins.
- Express with Equation: During level , Ezra found gold coins, and Zoe found gold coins. At the end of the level, they both had the same number of gold coins. We can express this with the equation: $(\frac{\(2\)}{\(3\)})z + \(32\) = z + \(6\).
- Solve for z: Now we need to solve the equation for z. First, we subtract \((\frac{2}{3})z\) from both sides to get all the z terms on one side:\(\newline\)\((\frac{2}{3})z + 32 - (\frac{2}{3})z = z + 6 - (\frac{2}{3})z\)\(\newline\)This simplifies to:\(\newline\)\(32 = (\frac{1}{3})z + 6\)
- Find \(z\): Next, we subtract \(6\) from both sides to isolate the \(z\) term:\(\newline\)\(32 - 6 = \frac{1}{3}z + 6 - 6\)\(\newline\)This simplifies to:\(\newline\)\(26 = \frac{1}{3}z\)
- Find \(z\): Next, we subtract \(6\) from both sides to isolate the \(z\) term:\(\newline\)\(32 - 6 = \frac{1}{3}z + 6 - 6\)\(\newline\)This simplifies to:\(\newline\)\(26 = \frac{1}{3}z\)To find \(z\), we multiply both sides by \(3\):\(\newline\)\(3 \times 26 = z\)\(\newline\)This gives us:\(\newline\)\(z = 78\)
More problems from Solve linear equations with variables on both sides: word problems
QuestionGet tutor help
QuestionGet tutor help
QuestionGet tutor help
QuestionGet tutor help
QuestionGet tutor help
QuestionGet tutor help
QuestionGet tutor help