Question

Q³ Write a pair of simultaneous equations and use them to solve: A wallet contains 34 notes, all of which are either $5 or $10 notes. The total value of the money is $285. How many $10 notes are there?

Answer 1

To solve the problem, we can write a pair of simultaneous equations and solve them using the method of substitution.

Step-by-step explanation:

Simultaneous Equations

Let x be the number of $5 notes and y be the number of $10 notes. We can write the following pair of simultaneous equations:

Equation 1: x + y = 34

Equation 2: 5x + 10y = 285

To solve these equations, we can use the method of substitution or elimination. Let's solve them using the method of substitution:

Method of Substitution

From Equation 1, we have x = 34 - y. Substitute this value of x into Equation 2:

1. 5(34 - y) + 10y = 285
2. Simplify the equation:
3. 170 - 5y + 10y = 285
4. Combine like terms:
5. 5y = 115
6. Divide both sides by 5:
7. y = 23

So, there are 23 $10 notes in the wallet.