Answer:
£15.10
x + 20
64 counters in the bag
Total money = £21.30
Step-by-step explanation:
20p = £0.20
50p = £0.50
100p = £1.00
Total value:
⇒ 8 × 20p + 5 × 50p + 11 × £1 = 8 × 20p + 5 × 50p + 11 × 100p
= 160p + 250p + 1100p
= 1510p
= £15.10
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20 more than x: x + 20
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If one quarter of the counters in a bag are yellow, and there are 16 yellow counters in the bag:
⇒ total number of counters in the bag = 16 × 4 = 64
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Let x = number of 20p coins
Let y = number of 50p coins
Let z = number pf £1.00 coins
Given:
- 20p coins are worth £2.80
⇒ 0.20x = 2.80
⇒ x = 2.80 0.20
⇒ x = 14
Therefore, there are 14 twenty pence coins.
Given:
- One third of the coins are 20p coins
We have calculated that there are 14 twenty pence coins, therefore:
⇒ total number of coins = number of 20p × 3
= 14 × 3
= 42
As the total number of coins is 42:
⇒ x + y + z = 42
⇒ 14 + y + z = 42
⇒ y + z = 42 - 14
⇒ y + z = 28
Therefore, the total number of 50p and £1 coins is 28.
Given:
- 10 more 50p coins than £1 coins
⇒ y = z + 10
Substitute y = z + 10 into y + z = 28 and solve for z:
⇒ (z + 10) + z = 28
⇒ 2z + 10 = 28
⇒ 2z = 18
⇒ z = 9
Therefore, there are 9 one pound coins
total number of coins:
⇒ x + y + z = 42
substituting the found values of x and z:
⇒ 14 + y + 9 = 42
⇒ 23 + y = 42
⇒ y = 19
Therefore, there are 19 fifty pence coins
20p coins = 14
50p coins = 19
£1 coins = 9
Therefore, total money:
= 14 × 20p + 19 × 50p + 9 × 100p
= 280p + 950p + 900p
= 2130p
= £21.30
