Originally Answered: Math problem.fairly easily problem buy my brain seems to not work today:) Help with the math problem?
Jane's weekly pay is 2/3 of Mary's.
Let's say Jane's weekly pay is X, and Mary's weekly pay is Y.
That means X = 2/3Y, from the first statement, and because "is" means =.
This is one equation.
The next equation you can find is that Jane's weekly pay and Mary's weekly pay is $1200.
That means X + Y = 1200, since you're just using variables to represent values.
Since X = 2/3Y, you can substitute it in that second equation for X to get:
(2/3Y) + Y = 1200
Then you simplify it to get:
1 2/3Y = 1200.
Then divide both sides by 1 and 2/3 to get:
Y = 720
Since Y is Mary's weekly pay, that means Mary's weekly pay is $720. That's one person's weekly pay found. Now to find the other, you just substitute Y = 720 into the the first equation for Y to get:
X = 2/3(720)
Then multiply 2/3 by 720 to get:
X = 480
Since X is Jane's weekly pay, that means Jane's pay is $480.
$480 is 2/3 of $720, so that satisfies the statement that says Jane's pay is 2/3 of Mary's pay.
Add $480 and $720 together and you get $1200, which satisfies the statement that together they earn $1200.
Therefore, your answers are justified and are correct.
2. Let us say the number of records is Nx and the number of tapes is Ny. Don't worry about how much they cost now; just focus on creating equations.
Since he sold 90 more tapes than records, that means the number of tapes is 90 more than the number of records. Therefore:
Ny = Nx + 90
Remember, Ny is the number of tapes, and Nx is the number of records.
Now, he sold both tapes and records for $2100.
The number of tapes multiplied by the cost of each tape would equal how much all the tapes cost, right?
This is represented by:
(6)Ny = Total cost of tapes
And the same goes for the records: the number of records multiplied by the cost of each record would equal the cost of all the records.
This is represented by:
(9)Nx = Total cost of records
If you add the total cost of tapes and the total cost of records together, then you get the total sale, right? And the total sale is $2100.
So that means:
(6)Ny + (9)Nx = 2100
Now take the first equation which was Ny = Nx + 90 and substitute it in for Ny to get:
(6)(Nx + 90) + (9)Nx = 2100
Then simplify it by multiplying 6 with Nx and 90 to get:
(6)Nx + 540 + (9)Nx = 2100
Then add the common variables together to get:
(15)Nx + 540 = 2100
Then subtract 540 from both sides to get:
(15)Nx = 1560
Then divide both sides by 15 to get:
Nx = 104
Which means that the number of records is 104. That is how many records he sold. Now to find the number of tapes, substitute Nx = 104 into the very first equation you made to get:
Ny = 104 + 90
Which simplifies to:
Ny = 194
Which means that the number of tapes he sold is 194. Now you can answer the question with the number of records (104) and tapes (194).
Answering these kinds of questions usually involve the substitution method (and sometimes the elimination method). If you're not clear on how they work, just ask your teacher to go more in depth on that subject.