Answer:
1. There are 70 dimes and 33 quarters
2. There are 42 dimes and 52 quarters
Step-by-step explanation:
Question 1:
Number of coins: 103
Vaiue of coins = $15.25
Required
Number of Dimes and Quarters;
Let D =Dimes and Q =Quarters
The total coins is represented as:
[tex]D + Q = 103[/tex] ----------------- Equation 1
1 dime is equivalent to $0.10 and 1 quarter is equivalent to $0.25; So
[tex]0.1D + O.25Q = 15.25[/tex] -------------------- Equation 2
Make D the subject of formula in equation 1
[tex]D = 103 - Q[/tex]
Substitute 103 - Q for D in equation 2
[tex]0.1(103 - Q) + 0.25Q = 15.25[/tex]
Open bracket
[tex]0.1*103 - 0.1 * Q + 0.25Q = 15.25[/tex]
[tex]10.3 - 0.1Q + 0.25Q = 15.25[/tex]
[tex]10.3 + 0.15Q = 15.25[/tex]
Subtract 10.3 from both sides
[tex]10.3 - 10.3 + 0.15Q = 15.25 - 10.3[/tex]
[tex]0.15Q = 15.25 - 10.3[/tex]
[tex]0.15Q = 4.95[/tex]
Divide both sides by 0.15
[tex]\frac{0.15Q}{0.15} = \frac{4.95}{0.15}[/tex]
[tex]Q = \frac{4.95}{0.15}[/tex]
[tex]Q = 33[/tex]
Recall that [tex]D = 103 - Q[/tex]
[tex]D = 103 - 33[/tex]
[tex]D = 70[/tex]
Hence, there are 70 dimes and 33 quarters
Question 2:
Number of coins: 94
Vaiue of coins = $17.2
Required
Number of Dimes and Quarters;
Let D =Dimes and Q =Quarters
The total coins is represented as:
[tex]D + Q = 94[/tex] ----------------- Equation 1
1 dime is equivalent to $0.10 and 1 quarter is equivalent to $0.25; So
[tex]0.1D + O.25Q = 17.2[/tex] -------------------- Equation 2
Make D the subject of formula in equation 1
[tex]D = 94 - Q[/tex]
Substitute 94 - Q for D in equation 2
[tex]0.1(94 - Q) + 0.25Q = 17.2[/tex]
Open bracket
[tex]0.1*94 - 0.1 * Q + 0.25Q = 17.2[/tex]
[tex]9.4 - 0.1Q + 0.25Q = 17.2[/tex]
[tex]9.4 + 0.15Q = 17.2[/tex]
Subtract 9.4 from both sides
[tex]9.4 - 9.4 + 0.15Q = 17.2 - 9.4[/tex]
[tex]0.15Q = 17.2 - 9.4[/tex]
[tex]0.15Q = 7.8[/tex]
Divide both sides by 0.15
[tex]\frac{0.15Q}{0.15} = \frac{7.8}{0.15}[/tex]
[tex]Q = \frac{7.8}{0.15}[/tex]
[tex]Q = 52[/tex]
Recall that [tex]D = 94 - Q[/tex]
[tex]D = 94 - 52[/tex]
[tex]D = 42[/tex]
Hence, there are 42 dimes and 52 quarters
