Sergio has p paintings in his art collection. He and other local painting collectors agreed to donate a total of 48 paintings to the local museum. Each of the 12 collectors will donate the same number of paintings. How many paintings will Sergio have in his art collection after his donation? Write your answer as an expression.
Answers
Since there are 48 paintings being donated by 12 collectors, then we can say that each collector will donate 4 paintings.
This means that Sergio will have 4 less paintings then he had before, which was represented by . Thus, our expression is now
.
The number of paintings Sergio will have in his art collection after his donation is p - 4
Given:
Number of Sergio's paintings = p
Total number of paintings to donate = 48
Number of collectors to donate (including Sergio) = 12
Number of paintings donated by each collector = Total number of paintings to donate ÷ Number of collectors to donate
= 48 ÷ 12
= 4 paintings per collector
Therefore,
Number of paintings Sergio will have in his art collection after his donation = Number of Sergio's paintings - Number of paintings donated by each collector
= p - 4
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Exercise #1:
Point H = (–2, 2)
Point J = (–2, –3)
Point K = (3, –3)
It would be very helpful if you could take a pencil and a piece
of paper, and sketch a graph with these points on it. Then
you'd immediately see what's going on.
Notice that points H and J have the same x-coordinate, but
different y-coordinates, so they're on the same vertical line.
Notice that points J and K have different x-coordinates but
the same y-coordinate, so they're on the same horizontal line.
Notice that point-J is on both the horizontal line and the vertical
line, so the lines meet there, and they're perpendicular.
Point-J is one corner of the square.
H is another corner of the square. It's 5 units above J.
K is another corner of the square. It's 5 units to the right of J.
The fourth corner is (2, 3) ... 5 to the right of H,
and 5 above K.
____________________________________
Exercise #2:
Point H = (6, 2)
Point J = (–2, –4)
Point K = (-2, y) .
It would be very helpful if you could take a pencil and a piece
of paper, and sketch a graph with these points on it. Then
you'd immediately see what's going on.
Notice that points J and K have the same x-coordinate, but
different y-coordinates, so they're on the same vertical line.
We need K to connect to point-H in such a way that it's on
the same horizontal line as H. Then the vertical and horizontal
lines that meet at K will be perpendicular, and we'll have the
right angle that we need there to make the right triangle.
So K and H need to have the same y-coordinate.
H is the point (6, 2). So K has to be up at (2, 2) .
____________________________________________
Exercise #3:
Point H = (-6, 2)
Point J = (–6, –1)
Point K = (4, 2) .
It would be very helpful if you could take a pencil and a piece
of paper, and sketch a graph with these points on it. Then
you'd immediately see what's going on.
This exercise is exactly the same as #1, except that it's a
rectangle instead of a square. It's still make of horizontal
and vertical lines, and that's all we need to know in order
to solve it.
Notice that points H and J have the same x-coordinate, but
different y-coordinates, so they're on the same vertical line.
Notice that points H and K have different x-coordinates but
the same y-coordinate, so they're on the same horizontal line.
Notice that point-H is on both the horizontal line and the vertical
line, so the lines meet there, and they're perpendicular.
Point-H is one corner of the rectangle.
J is another corner of the rectangle. It's 3 units below H.
K is another corner of the square. It's 4 units to the right of H.
The fourth corner is (2, -1) ... 4 to the right of J,
and 3 below K.
Answers
Hope this helps.
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