Respuesta :
Word problem are exercises in mathematics presented in common language rather than mathematical symbols
The coins in the bank are 8 pennies, 12 nickels, 15 dimes, and 6 quarters
The given parameters are;
Number of coins in Asa's piggy bank = 41 coins
Total amount of the coins (in the piggy bank) = $3.68
Number of quarters = Half the number of nickels
Number of dimes = 3 + Number of nickels
The rest of the coins in the bank = Pennies
Required:
The number of pennies, nickels, dimes, and quarters in the bank
Solution:
Let q represent the number of quarters, let n represent the number of nickels, let d represent the number dimes, and let p, represent the number of pennies, we have;
q = 0.5·n...(1)
d = 3 + n...(2)
q + n + d + p = 41...(3)
n = $0.5, p = $0.01, q = $0.25, d = $0.1
0.25·q + 0.05·n + 0.1·d + 0.01·p = 3.68...(4)
Therefore, there are four equations with four unknowns
Plugging in the values of q, and d from equation (1) and (2) in equation (3) gives;
0.5·n + n + (3 + n) + p = 41
2.5·n + p + 3 = 41
p = 38 - 2.5·n...(5)
Plugging in the values of q, d, and p in n in equation (4), gives;
0.25·(0.5·n) + 0.05·n + 0.1·(3 + n) + 0.01·(38 - 2.5·n) = 3.68
0.25·n = 3.68 - 0.68
[tex]n = \dfrac{3.00}{0.25} = 12[/tex]
The number of nickel, n = 12 nickels
Number of quarters, q = 0.5·n = 0.5 × 12 = 6
The number of quarters, q = 6 quarters
Number of dimes, d = 3 + n = 3 + 12 = 15
The number of dimes, d = 15 dimes
q + n + d + p = 41
p = 41 - (q + n + d)
∴ p= 41 - (6 + 12 + 15) = 8
The number of pennies, p = 8 pennies
Therefore, there are 8 pennies, 12 nickels, 15 dimes, and 6 quarters in his piggy bank
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