Maggie has only dimes and quarters in her purse. She has 27 coins with a total value of $4.05.
How many dimes does Maggie have in her purse?
Maggie has 20 dimes in her purse.
Wrong again Mr. bot
If Maggie has 20 dimes, then she must have 7 quarters
and she would have $2.00 + $1.75 or $3.75 , not $4.05 as needed
correct solution as done by a human:
d+q = 27
20d + 25q = 405
solving this system gives a positive and a negative answer
So the question is bogus to begin with.
To solve this problem, we can use a system of equations. Let's let the number of dimes be represented by "D" and the number of quarters be represented by "Q".
1. The first equation represents the total number of coins: D + Q = 27
2. The second equation represents the total value of the coins: 0.10D + 0.25Q = 4.05
Now, let's solve this system of equations to find the values of D and Q.
First, we'll solve equation 1 for D: D = 27 - Q
Next, let's substitute the value of D in equation 2: 0.10(27 - Q) + 0.25Q = 4.05
Distribute: 2.70 - 0.10Q + 0.25Q = 4.05
Combine like terms: 0.15Q = 1.35
Divide both sides by 0.15: Q = 1.35 / 0.15
Q = 9
Now, substitute the value of Q back into D = 27 - Q:
D = 27 - 9
D = 18
Therefore, Maggie has 18 dimes in her purse.
Video streaming company A charges a one-time $40 membership fee and $2 per video stream. Video streaming company B charges a one-time $20 membership fee and $4 per video stream.
Let the variable s represent the amount of videos streamed and let the variable c represent the cost.
For how many video streams will the cost be the same for both companies?
Which system of equations can be used to solve this problem?