Q: A chemist needs to mix a solution that is 30% acid with one that is 10% acid to obtain 20 liters of a 25% acid solution. Which equation models the amount of 30% solution needed ($$x$$ liters)?

$$0.3x + 0.1(20 - x) = 0.25 \times 20$$

Question 1

Translate the following phrase into an algebraic expression: 'Seven more than twice a number.'

Accepted Answer

$$2x + 7$$

Question 2

Which equation models the statement: 'Four subtracted from six times a number is 68'?

Accepted Answer

$$6x - 4 = 68$$

Question 3

A taxi charges $$2.00 to turn on the meter plus 0.25 $$for each eighth of a mile. If you have $10.00, how many eighths of a mile can you go?

Accepted Answer

$$32$$

Question 4

After a 40% price reduction, an exercise machine sold for $564. What was the original price?

Accepted Answer

$$940$$

Question 5

Which of the following is the correct algebraic translation for 'The sum of a number and five, divided by three'?

Accepted Answer

$$\frac{x + 5}{3}$$

Question 6

If the sum of two consecutive integers is 145, what are the integers?

Accepted Answer

$$72$$ and $$73$$

Question 7

Which step should you perform first when solving a word problem according to the recommended strategy?

Accepted Answer

Read the problem carefully several times and restate it in your own words.

Question 8

Translate the phrase 'Three times the difference of a number and four' into an algebraic expression.

Accepted Answer

$$3(x - 4)$$

Question 9

A store reduces the price of a jacket by 25%. If the sale price is $90, what was the original price?

Accepted Answer

$$120$$

Question 10

Which equation would you use to solve: 'The sum of twice a number and 11 is equal to 35'?

Accepted Answer

$$2x + 11 = 35$$

Question 11

A chemist needs to mix a solution that is 30% acid with one that is 10% acid to obtain 20 liters of a 25% acid solution. Which equation models the amount of 30% solution needed ($$x$$ liters)?

Accepted Answer

$$0.3x + 0.1(20 - x) = 0.25 	imes 20$$

Question 12

If $$x$$ represents the number of miles you can travel in a taxi with $$y$$ dollars, and the taxi charges $$2 to $$start plus $$0.25$$ per eighth of a mile, which equation models this scenario?

Accepted Answer

$$2 + 0.25x = y$$

Question 13

A number decreased by 15 is equal to twice the number increased by 3. What is the number?

Accepted Answer

$$-18$$

Question 14

Which of the following is the correct translation for 'The quotient of a number and 5, increased by 7'?

Accepted Answer

$$\frac{x}{5} + 7$$

Question 15

A student scored 12 points less than twice the number of points another student scored. If the total points scored by both students is 48, how many points did each student score?

Accepted Answer

$$20$$ and $$28$$

Linear Equations and Inequalities in One Variable: Problem Solving and Algebraic Translation

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