a ) A tourist visits Oman and exchanges 5 0 0 OMR into two different currencies: USD and EUR. She exchanges part of the money at the rate of 1 OMR = A USD and the rest at the rate of 1 OMR = B EUR.

Question

a ) ﻿A tourist visits Oman and exchanges 5 0 0 ﻿OMR into two different currencies: USD and EUR. She exchanges part of the money at the rate of 1 OMR = A USD and the rest at the rate of 1 OMR = B ﻿EUR. If she ends up with a total of 1 2 7 0 ﻿units of foreign currency, how much money in OMR did she exchange into USD and EUR, respectively? A = 1 6 4 B = 1 8 . 6 Solve the above problem by using any of the two given methods and make sure that the answers are the same Elimination Method ﻿Substitution Method *Give me explanation and calculation step by step clealry with final answe

VIPSolutions · Accepted Answer

Let's break down the problem step by step:

**Given:**
- Total OMR to exchange: $500$ OMR
- She exchanges some into USD at rate: $1$ OMR = **164** USD (*A = 164*)
- The rest is exchanged into EUR at rate: $1$ OMR = **18.6** EUR (*B = 18.6*)
- Total received in foreign currencies: **1270** units (combined USD and EUR)

Let:
- $x$ = OMR exchanged into USD
- $y$ = OMR exchanged into EUR

So:
1. $x + y = 500$                                                              (1)
2. $164x + 18.6y = 1270$                                                       (2)

We will solve using both **elimination** and **substitution** methods.

---

## **A) Elimination Method**

**Step 1:** Multiply equation (1) by 18.6 to align the "y" coefficients for elimination.

$$
x + y = 500 \implies 18.6x + 18.6y = 9300
$$

Now write the system:
$$
\begin{cases}
164x + 18.6y = 1270 \quad\quad (2)\
18.6x + 18.6y = 9300
\end{cases}
$$

**Step 2:** Subtract the second from the first to eliminate $y$:

$$
(164x + 18.6y) - (18.6x + 18.6y) = 1270 - 9300
$$
$$
(164x - 18.6x) + (18.6y - 18.6y) = -8030
$$
$$
145.4x = -8030
$$
$$
x = \frac{-8030}{145.4}
$$
$$
x \approx -55.23
$$

**Step 3:** Substitute $x$ back into equation (1):

$$
x + y = 500
$$
$$
-55.23 + y = 500
$$
$$
y = 500 + 55.23
$$
$$
y \approx 555.23
$$

---

## **B) Substitution Method**

**Step 1:** From equation (1): $x + y = 500 \implies x = 500 - y$

**Step 2:** Substitute into equation (2):

$$
164x + 18.6y = 1270
$$
$$
164(500 - y) + 18.6y = 1270
$$
$$
164 \times 500 - 164y + 18.6y = 1270
$$
$$
82000 - 164y + 18.6y = 1270
$$
$$
82000 - 145.4y = 1270
$$
$$
-145.4y = 1270 - 82000
$$
$$
-145.4y = -80730
$$
$$
y = \frac{-80730}{-145.4}
$$
$$
y \approx 555.23
$$

**Step 3:** $x = 500 - y$:

$$
x = 500 - 555.23 = -55.23
$$

---

## **Final Answers**

- **OMR exchanged into USD ($x$)**: $\boxed{-55.23\ \text{OMR}}$
- **OMR exchanged into EUR ($y$)**: $\boxed{555.23\ \text{OMR}}$

---

### **Explanation**

- Both methods give the same result.
- **However, a negative value for $x$ (OMR exchanged into USD) indicates that the numbers or the rates provided are unrealistic for a currency exchange.** Typically, exchange rates are less than 5 for USD/OMR or EUR/OMR, not 164 or 18.6.
- But mathematically, this is how you solve the system.

---

### **Summary Table**

| Method        | OMR to USD ($x$) | OMR to EUR ($y$) |
|---------------|--------------------|--------------------|
| Elimination   | $-55.23$         | $555.23$         |
| Substitution  | $-55.23$         | $555.23$         |

**Both methods yield the same answer.**

---

If you have different rates or units for A and B, please double-check and provide the correct information.

✨ VIPSolutions

Question:

Final Answer:

📢 Instructions:

Study Help, Fast Answers

✨ VIPSolutions

Question:

Final Answer:

📢 Instructions:

Related Answers

Study Help, Fast Answers