the cost of three markers and two pencils is 1.80
the cost of four markers and six pencils is 2.90
what is the cost of each item?
3x+4y=1.80
4x+6y=2.90
Do you know how to use elimination?
uhm no. explain the steps please?
Ok, so if you make markers "x" and pencils "y", you get
3x+4y=1.80
4x+6y=2.90
Then you use elimination (by figuring out what to multiply one or both equations by to get rid of one of the variables, either x or y).
Multiplying the top equation by -4
and the bottom equation by 3 to eliminate the x's gives us
-12x-16y=-7.2
12x+18y=8.7
Add the equations together
2y=1.5
Divide both sides by 2
y=?
Plug that back into any of your equations to solve for x.
Once you get your answers, feel free to post them if you want them checked.
thanks so much. do you have time for one more problem ?
Sure, are you still on?
To solve this problem, we can set up a system of equations. Let's say the cost of one marker is represented by "m" and the cost of one pencil is represented by "p".
From the first statement, we know that three markers and two pencils cost $1.80. This can be expressed as:
3m + 2p = 1.80
From the second statement, we know that four markers and six pencils cost $2.90. This can be expressed as:
4m + 6p = 2.90
Now we have a system of two equations. We can solve this system either by substitution or elimination. Let's use the elimination method:
Multiply the first equation by 3 and the second equation by 2 to make the coefficients of "m" the same:
(3 * 3m) + (3 * 2p) = (3 * 1.80)
(2 * 4m) + (2 * 6p) = (2 * 2.90)
This simplifies to:
9m + 6p = 5.40
8m + 12p = 5.80
Next, multiply the first equation by -2, so we can eliminate the "m" variable when we add the equations:
(-2 * 9m) + (-2 * 6p) = (-2 * 5.40)
This simplifies to:
-18m - 12p = -10.80
Now, we can add the two equations:
(-18m - 12p) + (8m + 12p) = -10.80 + 5.80
This simplifies to:
-10m = -5
Finally, we can solve for "m" by dividing both sides of the equation by -10:
m = -5 / -10
m = 0.50
Now that we have the value of "m," we can substitute it back into one of the original equations to solve for "p." Let's use the first equation:
3(0.50) + 2p = 1.80
1.50 + 2p = 1.80
Subtract 1.50 from both sides of the equation:
2p = 1.80 - 1.50
2p = 0.30
Now, divide both sides of the equation by 2 to solve for "p":
p = 0.30 / 2
p = 0.15
Therefore, the cost of each marker is $0.50, and the cost of each pencil is $0.15.