Download Grid In Answers to Algebra Problems

strategy
11
Grid In Answers to Algebra Problems
To answer some TASC questions, you will fill in a grid instead of choosing from four options. To record an
answer, first fill in the boxes at the top of the columns in the grid. Then, fill in the matching circle for each
column. It is the circles that are scored, so it is very important to fill them in carefully.
There are a few rules for using the grids:
• You can start an answer in any column as long as it fits within the 5 columns.
• If your answer contains a decimal point or a fraction slash, that element must have its own column.
• No other symbols can be used.
• A mixed number must be entered as an improper fraction or a decimal.
(1 12 could be entered as either 32 or 1.5)
Example
TASC Problem
The second of two numbers is four times the first. Their
sum is 65. What is the greater number?
A soccer player shot at least 12 times in one game.
The number of missed goals was eight more than the
number of goals scored. What is the smallest number
of goals the player could have scored?
Think: I can use algebraic language to write an
equation, and then solve it.
Think: I can use algebraic language to write an
inequality and solve it.
Step 1:Write an expression for each number.
Let n = the first number
Let 4n = the second number
Step 1:Write expressions for goals scored and missed
goals.
Step 2:Write an equation showing the sum of the
numbers is 65.
Let g = goals scored
Let g + 8 = goals missed
n + 4n = 65
Step 2:Write an inequality to show the number of
shots taken.
Step 3: Solve the equation.
n + 4n = 65
5n = 65
n = 13
4n = 4(13) = 52
SOLUTION: 52 Step 3: Solve the inequality.
5 2
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g + g + 8 ≥ 12
2g + 8 ≥ 12
2g ≥ 4
g≥2
ANSWER: The player scored at least
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testwise
Before you grid in your answer, be sure to reread the problem. Are you answering the correct question? Make sure you
have addressed the question you were asked.
26 Unit 2: Equations, Functions, and Inequalities
© New Readers Press. All rights reserved.
Step 4:Answer the question,
“What is the greater number?”
g + g + 8 ≥ 12
Apply the Strategy
Write your answers in the grid. For all questions, first decide what unknown quantity the variable will
represent.
1.The length of a tennis court is 78 feet.
This is 3 less than 3 times the width
of the court. What is the width of
the court?
Mark your answer in the circles of
the grid.
Let x =
2.Tally earns $56 per day. This is at least
$10 more per day than Frank earns.
At most, how much does Frank earn?
Mark your answer in the circles of
the grid.
Let x =
3.Hannah has 64 stamps in her
collection. The number of new
stamps is 11 less than 4 times the
number of old stamps. How many
new stamps does she have?
Mark your answer in the circles of
the grid.
Let x =
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4.Rad is 5 more than twice Brian’s age
in years. The sum of their ages is 35.
How old is Rad?
Mark your answer in the circles of
the grid.
Let x =
5.In a 30-minute television show, the
number of minutes of programming
is six more than twice the number of
minutes of advertisement. How many
minutes of programming are there?
Mark your answer in the circles of
the grid.
Let x =
6.At Bicycle Mart, 40 fewer bicycles
were sold in May than were sold
in April. The total number sold in
April and May was less than the 120
bicycles sold in March. What is the
maximum number of bicycles that
could have been sold in May?
Mark your answer in the circles of
the grid.
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Let b =
© New Readers Press. All rights reserved.
Answers start on page 44. Unit 2: Equations, Functions, and Inequalities
27
Grid in Answers to Algebra Problems 1. 2 . 0 1 2 3 4 5 6 7 8 9 2. 4 . 0 1 2 3 4 5 6 7 8 9 3. 4 . 0 1 2 3 4 5 7 / . 0 1 2 3 4 5 6 7 8 9 6 / . 0 1 2 3 4 5 6 7 8 9 9 / . 0 1 2 3 4 5 / . 0 1 2 3 4 5 6 7 8 9 / . 0 1 2 3 4 5 6 7 8 9 / . 0 1 2 3 4 5 / . 0 1 2 3 4 5 6 7 8 9 / . 0 1 2 3 4 5 6 7 8 9 / . 0 1 2 3 4 5 . 0 1 2 3 4 5 6 7 8 9 . 0 1 2 3 4 5 6 7 8 9 . 0 1 2 3 4 5 Step 1: Write expressions for length and width of court Let x = width of court Let 3x – 3 = length of court Step 2: Write an equation to show length of court 3x – 3 =78 Step 3: Solve for x 3x – 3 = 78 3x = 81 x = 27 Step 1: Write expressions for each person’s pay Let x = Frank’s pay Let 56 = Tally’s pay Step 2: Write an inequality showing Tally’s pay is at least $10 more than Frank’s 56 ≥ 10 + x Step 3: Solve for x 56 ≥ 10 + x 46 ≥ x Step 1: Write expressions for the number of old stamps and for new stamps Let x = number of old stamps Let 4x – 11 = number of new stamps Step 2: Write an equation for the sum of old and new stamps x + (4x -­‐11) = 64 Step 3: solve for x x + (4x -­‐11) = 64 5x = 75 x = 25 Step 4: Solve for new stamps 6 7 8 9 4. 2 . 0 1 2 3 4 5 6 7 8 9 5. 2 . 0 1 2 3 4 5 6 7 8 9 6. 4 . 0 1 2 3 4 6 7 8 9 5 / . 0 1 2 3 4 5 6 7 8 9 2 / . 0 1 2 3 4 5 6 7 8 9 0 / . 0 1 2 3 4 6 7 8 9 / . 0 1 2 3 4 5 6 7 8 9 / . 0 1 2 3 4 5 6 7 8 9 / . 0 1 2 3 4 6 7 8 9 / . 0 1 2 3 4 5 6 7 8 9 / . 0 1 2 3 4 5 6 7 8 9 / . 0 1 2 3 4 6 7 8 9 . 0 1 2 3 4 5 6 7 8 9 . 0 1 2 3 4 5 6 7 8 9 . 0 1 2 3 4 4x – 11 = 4(15) – 11 = 49 Step 1: Write expressions for each person’s age Let x = Brian’s age Let 2x + 5 = Rad’s age Step 2: Write an equation for the sum of their ages x + 2x + 5 = 35 Step 3: Solve for x x + 2x + 5 = 35 3x = 30 x = 10 Step 4: Solve for Rad’s age 2x + 5 = 2(10) + 5 2x + 5 = 25 Step 1: Write an expression for number of minutes of program and for number of minutes of advertisement Let x = minutes of advertisement Let 6 + 2x = minutes of programming Step 2: Write an equation for the sum of advertisement and programing minutes x + 6 + 2x = 30 Step 3: Solve for x x + 6 + 2x = 30 6 + 3x = 30 3x = 24 x = 8 Step 4: Solve for programming 6 + 2x = 6 + 2(8) 6 + 2x = 22 Step 1: write expressions for number of bicycles sold in March, April and May Let b = bicycles sold in April Let b – 40 = bicycles sold in May Let 120 = bicycles sold in March Step 2: Write an inequality showing the number of bicycles sold in April and May was less than the number sold in March b + b – 40 < 120 Step 3: Solve for b 5 6 7 8 9 5 6 7 8 9 5 6 7 8 9 5 6 7 8 9 5 6 7 8 9 b + b – 40 < 120 2b < 160 b < 80 Step 4: Solve for the maximum number of bicycles that could have been sold in May b – 40 = 80 – 40 b-­‐ 40 = 40