Find the value that makes the equation 2d + 4 = 12 true.
2 answers:
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So, we know the slope of the original equation is 4. So the perpendicular slope is the negative reciprocal, so it's -1/4. Then, the points have to be -3, 7. So when we plug that into our equation, we get
<u><em>Answer:</em></u>
The coordinate pair that represents this solution is (20 , 240)
<u><em>Explanation:</em></u>
<u>We are given that:</u>
1- Equation that represents amount paid on football team based on number of purchased footballs is:
y = 40 + 10x
2- Equation that represents amount paid on baseball team based on number of purchased baseballs is:
y = 200 + 2x
Now, Logan wants to spend the same amount of money on both teams. This means that the y value in both equations should be equal
He also wants to buy the same number of balls for the two teams. This means that the x value in both equations should also be equal.
Therefore, we would be getting the point of intersection between the two equations.
<u>To do this, we will start by equating the two equations and solving for x as follows:</u>
40 + 10x = 200 + 2x
10x - 2x = 200 - 40
8x = 160
x = 20
<u>Then, we will use the x to substitute in any of the two equations:</u>
<u>Substituting in the first equation:</u>
y = 40 + 10x = 40 + 10(20) = 240
<u>Substituting in the second equation (as a check):</u>
y = 200 + 2x = 200 + 2(20) = 240
<u>Based on the above calculations:</u>
If Logan bought 20 balls for each team, he will be spending $240 on each
Solution set is (20, 240)
Note: the graphical solution is attached.
Hope this helps :)
