Barney and Betty break into a parking meter with $3,95 in dimes and quarters in it (legal disclaimer: don't do this), and agree that Barney will get all the dimes,and Betty will get all the quarters. (Barney isn't terdbly bright.) Barney ends up with eight more coins than Betty. How much money did each get? Barney got $___ and Betty got $—-The picture I’m sending along is an example problem to help!! Example**Step 1: Understand the problem**The key information: Barney and Betty obtain a total of $4.80 in dimes and quarters. Barney will get all the dimes and Betty will get all the quarters. Barney ends up with six more coins than Betty.**Step 2: Devise a plan to solve the problem**Recall that dimes carry a numerical value of 10 cents which is equivalent to $0.10 and quarters carry a numerical value of 25 cents which is equivalent to $0.25.Let $ x $ be the number of Barney's coins. Since Barney ends up with six more coins than Betty, Betty will have $ (x - 6) $ coins.Make an equation.\[ $0.10x + $0.25(x - 6) = $4.80 \]**Step 3: Carry out your plan to solve the problem**Solve the equation for $ x $.\[ $0.10x = $0.25x - $0.25(6) = $4.80 \]Multiply.\[ $0.10x + $0.25x - $1.50 = $4.80 \]Combine like terms.\[ $0.35x - $1.50 = $4.80 \] **Example**1. **Add $1.50 to each side of the equation.** \[ 0.35x - 1.50 + 1.50 = 4.80 + 1.50 \] \[ 0.35x = 6.3 \]2. **Divide both sides of the equation by 0.35.** \[ \frac{0.35x}{0.35} = \frac{6.3}{0.35} \] \[ x = 18 \]3. **Conclusion** Therefore, Barney gets 18 dimes, which is equivalent to $1.80, and Betty gets 12 quarters, which is equivalent to $3.00.4. **Step 4: Check your answer.** We already know that Barney gets $1.80, and Betty gets $3.00. Together they get $4.80.---**Answer**Barney got $1.80 and Betty got $3.00.

Given: Barney and Betty obtain a total of $3.95 in dimes and quarters. Barney will get all the…

Barney and Betty break into a parking meter with $3,95 in dimes and quarters in it (legal disclaimer: don't do this), and agree that Barney will get all the dimes, and Betty will get all the quarters. (Barney isn't terdbly bright.) Barney ends up with eight more coins than Betty. How much money did each get? Barney got $___ and Betty got $

Barney and Betty break into a parking meter with $3,95 in dimes and quarters in it (legal disclaimer: don't do this), and agree that Barney will get all the dimes, and Betty will get all the quarters. (Barney isn't terdbly bright.) Barney ends up with eight more coins than Betty. How much money did each get? Barney got $___ and Betty got $

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

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Example

**Step 1: Understand the problem**

The key information: Barney and Betty obtain a total of $4.80 in dimes and quarters. Barney will get all the dimes and Betty will get all the quarters. Barney ends up with six more coins than Betty.

**Step 2: Devise a plan to solve the problem**

Recall that dimes carry a numerical value of 10 cents which is equivalent to $0.10 and quarters carry a numerical value of 25 cents which is equivalent to $0.25.

Let $ x $ be the number of Barney's coins. Since Barney ends up with six more coins than Betty, Betty will have $ (x - 6) $ coins.

Make an equation.

\[ $0.10x + $0.25(x - 6) = $4.80 \]

**Step 3: Carry out your plan to solve the problem**

Solve the equation for $ x $.

\[ $0.10x = $0.25x - $0.25(6) = $4.80 \]

Multiply.

\[ $0.10x + $0.25x - $1.50 = $4.80 \]

Combine like terms.

\[ $0.35x - $1.50 = $4.80 \]

**Example**

1. **Add $1.50 to each side of the equation.**

\[
0.35x - 1.50 + 1.50 = 4.80 + 1.50
\]

\[
0.35x = 6.3
\]

2. **Divide both sides of the equation by 0.35.**

\[
\frac{0.35x}{0.35} = \frac{6.3}{0.35}
\]

\[
x = 18
\]

3. **Conclusion**

Therefore, Barney gets 18 dimes, which is equivalent to $1.80, and Betty gets 12 quarters, which is equivalent to $3.00.

4. **Step 4: Check your answer.**

We already know that Barney gets $1.80, and Betty gets $3.00. Together they get $4.80.

---

**Answer**

Barney got $1.80 and Betty got $3.00.

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