Question

20 points!!!! Freya is collecting 50p and £1 coins. When she has 18 coins the value of them is £13.

Let x be the number of 50p coins and y the number of £1 coins. Write a pair of simultaneous equations for this.

Answer 1

• x + y = 18
• 0.5x +y = 13

Explanation:

The system of equations formalizes the given relationships regarding the number of coins and their value.

x + y = 18 . . . . . . Freya has 18 coins

0.50x +1.00y = 13 . . . . their value is £13

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Additional comment

The solution can be found by subtracting the second equation from the first:

0.5x = 5

x = 10

y = 18 -10 = 8

Freya has 10 50p coins and 8 £1 coins.