Peter has some 20-cent coins and 50-cent coins. The number of 20-cent coins is four times as many as the number of 50-cent coins. The value of the 20-cent coins is $11.40 more than the value of the 50-cent coins. How many fewer 50-cent coins than 20-cent coins does Peter have? (3 marks)
Answer: 114 coins
Let number of 50-cent coins = 1u Number of 20-cent coins = 4u
Value of 50-cent coins → 1u × 50c = 50u
Value of 20-cent coins → 4u × 20c = 80u
Difference in value → 80u - 50u = 30u
The value of the 20-cent coins is $11.40 more than the value of the 50-cent coins.
30u = $11.40 30u = 1140c 1u = 1140 ÷ 30 = 38
Difference in number of coins → 4u - 1u = 3u = 3 × 38 = 114
Answer: 114 coins
"The number of 20-cent coins is four times as many as the number of 50-cent coins. "
let 1u be number of 50 cent coins
number of 50¢ → 1u number of 20¢ → 4 x 1u = 4u
" The value of the 20-cent coins is $11.40 more than the value of the 50-cent coins."
value of 50¢ (units) → 1u x 50 = 50u
value of 20¢ (units) → 4u x 20 = 80u
difference (units) → 80u - 50u = 30u
difference → $11.40 = 1140¢
30u → 1140 1u → 1140 ÷ 30 = 38
difference in number of coins (units) → 4u - 1u = 3u
3u → 3 x 38 = 114