Hello! I have two math questions:
1.) Marcos has 28 coins that are all nickels (n) and dimes (d). The value of the coins is $2.05. Which system of equations can be used to find the number of nickels and the number the dimes?
A. n + d = 28
5n + 10d = 205
B. n + d = 28
10n + 5d = 2.05
C. n + d = 205
n + d = 28
D. 10n + 5d = 205
n + d = 28
2.) Two groups of students order burritos and tacos at a local restaurant. One order of 3 burritos and 4 tacos costs $11.33. The other order of 9 burritos and 5 tacos costs $23.56. Which system of equations represents this problem situation?
A. x + y = 7
x + y = 14
B. 3x + 4y = 11.33
9x + 5y = 23.56
C. 3x + 4y = 23.56
9x + 5y = 11.33
D. x + y = 12
x + y = 9
#1 should be obvious
since d is "dime", it has to be multiplied by 10 (10 cents in a dime)
and n is "nickels" it has to be multiplied by 5
So what do you think?
#2, Once you define what x and y represent, the answer should be obvious as well.
I would have used b and t instead of x and y.
So
#1 is A and #2 is D?
correct for #1, wrong for #2
#2
If x is cost of buritos, y is cost of tacos
"3 burritos and 4 tacos costs $11.33" --->3x+4y = 11.33
"9 burritos and 5 tacos costs $23.56" ----> 9x + 5y = 23.56
B !!!!
Now , how easy was that? Notice how I just translated the "math" into English ?
For the first question:
To find the number of nickels and the number of dimes, we can set up a system of equations based on the given information.
Let's use variables n for the number of nickels and d for the number of dimes.
Since Marcos has a total of 28 coins, the first equation is n + d = 28.
The value of the coins is $2.05. We know that nickels are worth 5 cents and dimes are worth 10 cents, so we can set up the second equation as 5n + 10d = 205 (converting dollars to cents).
Now we need to determine which system of equations matches the given information:
A. n + d = 28
5n + 10d = 205
B. n + d = 28
10n + 5d = 2.05
C. n + d = 205
n + d = 28
D. 10n + 5d = 205
n + d = 28
The correct answer is option A, because it correctly represents the relationships between the number of coins and their values.
Moving on to the second question:
Similar to the first question, we need to set up a system of equations to represent the problem.
Let's use variables x for the number of burritos and y for the number of tacos.
According to the given information, the first order of 3 burritos and 4 tacos costs $11.33. This can be expressed as the equation 3x + 4y = 11.33.
The second order of 9 burritos and 5 tacos costs $23.56, which can be written as the equation 9x + 5y = 23.56.
Now we need to determine which system of equations matches the given information:
A. x + y = 7
x + y = 14
B. 3x + 4y = 11.33
9x + 5y = 23.56
C. 3x + 4y = 23.56
9x + 5y = 11.33
D. x + y = 12
x + y = 9
The correct answer is option B, because it correctly represents the cost of the two orders in terms of the number of burritos and tacos.