| Problem |
Solution |
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1) Joe and Sue are planting trees in the park for Arbor Day. On the first day they planted
38 trees. Joe did not work the next day, but Sue planted the same number of trees that
she had planted the first day. Together Sue and Joe planted 60 trees over the two days.
What was the number of trees Joe planted? |
Let J = the number of trees Joe planted.
Let S = the number of trees Sue planted each day.
Then J + S = 38 (first day)
J + 2S = 60 (total planted)
Solve the first equation for S and substitute it into the second equation and solve for J =
S = 38 - J
J + 2(38 - J) = 60
-J = -16; J = 16 trees.
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2) One angle of a triangle has a measurement of 70 degrees. The ratio of the other two
angles of the triangle is 5 : 6. What are the measurements of the other 2 angles?
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1. Compute what the other 2 angles sum to: 110 degrees.
2. The smaller angle is 5/11 of this sum.
(5/11) x 110 = 50 degrees.
3. Find both angles = 50 and 60 degrees.
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3) Kara made this sequence of shapes with blocks:
If she continues this pattern, at what stage will she use 28 blocks in a shape? |
This is an arithmetic sequence.
1. Write out in a line the number of blocks in each stage:
6 8 10 . . .
2. Find the amount (d) added to each stage = 2
3. Use the equation for the nth term of an arithmetic sequence to find the term which has 28 blocks (the nth term):
an = a1 + d(n - 1).
28 = 6 + 2(n - 1) =
2n - 2 = 22
n = 12
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