Answer:
7 quarters
9 nickels
Step-by-step explanation:
Let q = number of quarters
Let n = number of nickels
Nickel = $0.05
Quarter = $0.25
Given: total of coins in the cup = 16
⇒ n + q = 16
Given: total inside the cup = $2.20
⇒ 0.05n + 0.25q = 2.20
Rewrite n + q = 16 to make n the subject:
⇒ n = 16 - q
Substitute n = 16 - q into 0.05n + 0.25q = 2.20 and solve for q:
⇒ 0.05(16 - q) + 0.25q = 2.20
⇒ 0.8 + 0.2q = 2.20
⇒ 0.2q = 1.4
⇒ q = 7
Now substitute found value for q into n = 16 - q and solve for n:
⇒ n = 16 - 7
⇒ n = 9
Therefore, there are 7 quarters and 9 nickels in the cup.
Answer: 9 nickels and 7 quarters
Step-by-step explanation:
Let N be the number of nickels in the cup
Let Q be the number of quarters in the cup
For the first equation, we will be using the total number of coins in the cup .
N + Q = 16
Q = 16 - N...Equation 1
We know that a nickel = 5 cents and a quarter is 25 cents. Now, substitute the number of nickels in in dollars
0.05 N + 0.25Q = 2.20...Equation 2
Use substitution to solve for two equations to solve for the problem:
[tex]\begin{aligned}0.05 N+0.25 Q &=2.20 \\0.05 N+(16-N)(0.25)=2.20 \\0.05 N+4-0.25 N=2.20 \\0.05 N-0.25 N &=2.20-4 \\-0.2 N &=-1.8 \\N &=9 \\\end{aligned}[/tex]
Now, substitute the number of nickels in in dollars in Equation 1 to get the number of quarters.
N + Q = 16
9 + Q = 14
Q = 16- 9
Q = 7
Therefore, there are 9 nickels and 7 quarters in the cup
