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Algebra Problems

#1 The perimeter of a rectangle is 144m. The length is 6m more than twice the width. Find the dimensions.

#2 Hockey teams receive 2 points when they win and 1 point when they tie. One season, a team won a championship with 61 points. They won 11 more games than they tied. How many wins and how many ties did they have?

#3 The perimeter of a rectangle is 160 inches. The length exceeds the width by 74 inches. Find the length and width.

#4 The Everton college store paid $1628 for a order of 44 calculators. The store paid $11 for each scientific calculator. The others, all graphing calculators, cost the store $55 each. How many of each type of calculators was order?

#5 Soybean meal is 12% protein; cornmeal is 6% protein. How many pounds of each should be mixed together in order to get 240-lb mixture that is 11% protein?

#6 Snooker lumber can covert logs into either lumber or plywood. In a given day, the mill turns out twice as many units of plywood as lumber. It makes a profit of $20 on a unit of lumber and $50 on a unit of plywood. How many of each unit must be produced and sold in order to make profit of $12120?

Solution Preview

Please see the attachment.
Six questions to be answered.
1. The perimeter of s rectangle is 144m. The length is 6m more than twice the width. Find the dimensions.
What is the length?
Simplify answer.
Answer
Let 'l' be the length and 'b' be the width of the rectangle. Given that length is 6m more than twice the width.
That is, l = 2b + 6 ------------ (1)
Perimeter of the rectangle is 144m.
That is, 2(l + b) = 144
Substituting the value of l from (1) in the above equation, we get,
That is, 2(2b + 6 + b) = 144
That is, 6b + 12 = 144
That is, 6b = 144 - 12 = 132
Therefore, b = 132/6 = 22
Substituting the value of b in (1), we get,
l = 2 * 22 + 6 = 50
Hence length = 50m and width = 22m.
2. Hockey teams receive 2 points when they win and 1 point when they tie. One season, a team won a championship with 61 points. They won 11 more games than they tied. How many wins and how many ties did they have?
What is the # of wins?
What is the # of ...

Solution Summary

The solution provides step by step method for the calculation of answers to algebra problems. Formula for the calculation is also included.

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