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4) Ms. Schultz passes out strawberries to her Spanish class. If she gives each student 6 strawberries,
she has 28 left. If she gives each student 8 strawberries, she has 4 left. How many strawberries does
Ms. Schultz have? |
1. Subtract the number left from passing out 8 strawberries from the number left after passing out 6 = ____ strawberries.
2. These were shared by ___ students so there are _____ students in her class.
3. Multiply this number of students by 8 and add 4 to get the total number of strawberries = _____.
4. Check this with the computation for 6 students.
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5) In the pattern of circles shown, each new encircling layer adds more circles. The layers alternate in color beginning with white, then grey, and then white. When the pattern has exactly 3 grey layers, how many circles of both colors are in the pattern?
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Method 1: Analyze the layering
The figure has 6 sides and with each additional layer still has 6 sides.
1. Each layer adds 1 to the length of a side, so the next gray layer has sides that are ____ circles long
and the next white layer has sides that are ____ circles long.
and the next gray layer has sides that are ____ circles long.
2. But the circles on the corners are shared by the adjacent sides, so ____ of them must be subtracted.
3. Doing this, the next gray layer has ____ circles on each side - _____ shared circles, leaving ____ circles in the gray layer.
4. The next white layer has ____ circles on each side - ____ shared circles, leaving ____ circles in the next white layer.
5. The next gray layer has ____ circles on each side - ____ shared circles, leaving ____ circles in the next white layer.
6. Adding these up gives us a total of _____ circles in the figure.
Method 2: Use the formula for the sum of an arithmetic sequence:
1. Write down the number of circles in each layer:
1 6 12 ...
2. Ignoring the one in the center, each layer adds 6 circles.
3. When the pattern has 3 grey circles it will have a total of 5 layers (ignoring the one in the middle).
4. The 5th term of this sequence is A5 = 6 + 6 (5 - 1) = 30
5. The formula for the sum of an arithmetic sequence is:
Sum = ((A1 + An) x n) / 2
6. So the sum is (6 + 30) x 5 / 2 = 18 x 5 = 90.
7. Add the one in the center and the total is 91.
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3) Maya loves dogs and is happy to dog sit for her neighbors.
She charges a small initial fee and then an hourly rate. Based
on the table, what is an expression that will let her quickly
compute how much she will earn for h hours of dog sitting for
one dog?