Jeremy had 34 nickels and quarters totaling $4.10. He had two less than twice as many nickels and quarters. How many of each did he have?
Do you mean? -
twice as many nickels AS quarters.
Sue S. Yes :/ Sorry
No, you mean two less than twice as many nickels as quarters; however, you don't need that information to work the problem.
n = # nickels
q = # quarters
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n + q = 34
5n + 25q = 410 Solve these two simultaneously.
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5n + 25(34-n) = 410
Solve and n = 22 and q = 12
check:
22*0.05 = $1.10
12*0.25 = 3.00
Total is $4.10.
You will see that the number of nickels is 2 less than 24 and 24 is 2 x # q = 24,
Dr.Bob222 thank you. I’m used to solving the top one. However, my teacher wants me to use the second equation. I did come to the class later than everyone else. So I don’t know how you put those numbers into the equation. But for now I’ll use the top one
I'm not sure what you mean by using the top equation or the second equation. You must use BOTH equations and solve them simultaneously.
#n + #q = 34 (eqn 1 tells you the total number of coins)
5*#n + 25*#q = 410 (eqn 2 tells you the value of the coins; i.e. 410 cents).
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Using eqn 1 solve for #q. That gives you #q = 34 - #n. Substitute that q into the q in eqn 2 as shown below.
5*#n + 25(34-#n) = 410
5*#n + 850 - 25^#n = 410
-20n = 410-850
-20n = -440
20n = 440
n = 440/20 = 22 = #nickels
Since n + q = 34 the q must be 34-22 = 12
i have the same question now in my algebra textbook. what grade you in me 7th
To solve this problem, we can set up a system of equations based on the information given.
Let's say the number of nickels Jeremy had is N, and the number of quarters is Q.
According to the problem, Jeremy had two less than twice as many nickels and quarters, which can be written as:
N + Q = 2(N + Q) - 2
Next, we know that Jeremy had a total of 34 nickels and quarters, so we can write another equation:
N + Q = 34
Now, we can solve the system of equations to find the values of N and Q.
Substitute the value of N + Q from the second equation into the first equation:
34 = 2(N + Q) - 2
34 = 2N + 2Q - 2
36 = 2N + 2Q
Now, subtract the second equation from the third equation:
0 = N + Q - 2N - 2Q
0 = -N - Q
Next, substitute the value of -N - Q from the fourth equation into the second equation:
34 = -N - Q
N = -34 - Q
Now substitute the value of N = -34 - Q into the first equation:
36 = 2(-34 - Q) + 2Q
36 = -68 - 2Q + 2Q
Combine like terms:
36 = -68
This equation is not true, which means there is no solution.
Therefore, there is no way Jeremy could have had 34 nickels and quarters totaling $4.10.