Practice Test 6 - Pre Algebra

20 questions. Answer them in any order, then submit to see your score and every explanation.

A stock price changed by $x$ dollars on Monday and by the opposite amount on Tuesday. On Wednesday, it changed by an amount whose absolute value equals $|x|$ . If the net change over three days was $+12$ dollars, what was Wednesday's change?
A rectangular garden has a perimeter of 60 feet. If the length is 8 feet more than twice the width, what system of equations models this situation where $l$ represents length and $w$ represents width?
Consider the expression $6x^2y - 4xy + 8x^2y - 12xy + 2$ . After combining like terms, which term has a coefficient that is a factor of all the other coefficients in the simplified expression?
A machine produces widgets at a rate of $\frac{7}{12}$ widgets per minute. If the machine operates at $\frac{4}{7}$ of its normal capacity for $\frac{3}{2}$ hours, how many widgets will it produce?
Sarah creates a pattern using squares and triangles. Row 1 has 1 square, Row 2 has 2 squares and 1 triangle, Row 3 has 3 squares and 3 triangles, Row 4 has 4 squares and 6 triangles. If this pattern continues, how many total shapes will be in Row 7?
The equation $ax + 5 = 3x + b$ has the solution $x = 2$ . If $a + b = 8$ , what are the values of $a$ and $b$ ?
A recipe calls for $\frac{1}{3}$ cup of flour for every $2$ servings. Sarah wants to make enough for $s$ servings, but she only has $\frac{2}{3}$ the amount of flour the recipe requires. Which expression represents the amount of flour Sarah has, in cups?
A temperature control system maintains safe operation when the temperature $T$ (in degrees Celsius) satisfies $-15 < T \leq 40$ . However, an alarm sounds when $T < -10$ or $T > 35$ . For which values of $T$ does the system operate safely but without an alarm?
Maria calculated that she spent 0.275 of her monthly budget on groceries and 18% of her budget on entertainment. What is the difference between these two expense categories expressed as a percentage?
A factory produces widgets at a rate where $12.7\%$ are defective. If the factory aims to ship $2,450$ non-defective widgets, approximately how many total widgets must they produce?
A researcher creates a box plot from survey data about daily screen time (in hours) for teenagers. The box plot shows Q1 = 4, median = 6, Q3 = 8, with whiskers extending to 2 and 11 hours. If the researcher wants to identify teenagers with "unusually high" screen time using the 1.5 × IQR rule, what is the minimum number of hours of daily screen time that would be considered unusually high?
Maria solved the equation $3x - 7 = 14$ and got $x = 3$ . When she substituted her answer back into the original equation to check, what value did she get for the left side of the equation?
Two similar parallelograms have perimeters in the ratio 7:4. If the larger parallelogram has an area of 147 square centimeters, what is the area of the smaller parallelogram?
A garden sprinkler system has three zones. Zone A uses $\frac{3}{8}$ of the total daily water allocation, Zone B uses $\frac{1}{6}$ of the total allocation, and Zone C uses the remaining water. If the system malfunctions and Zone A uses an additional $\frac{1}{12}$ of the total daily allocation, what fraction of the total daily allocation does Zone C now receive?
A machine produces widgets in batches. The first batch contains $2^2 \cdot 3^1$ widgets, the second batch contains $2^1 \cdot 3^3$ widgets, and the third batch contains $2^3 \cdot 5^2$ widgets. If all widgets from the three batches are to be packed into identical boxes with no widgets left over, what is the largest number of widgets that can be placed in each box?
In the linear equation representing her elevation over time, what does the slope represent and what mistake would lead someone to calculate it as $680$ feet per hour?
A phone plan costs $25 per month plus $0.05 per text message. Another plan costs $35 per month with unlimited texting. After how many text messages in a month would both plans cost the same amount?
A bicycle wheel has a radius of 14 inches. After the bicycle travels 500 feet, approximately how many complete rotations has the wheel made?
A trapezoid has an area formula $A = \frac{1}{2}(b_1 + b_2)h$ . If $b_1 = (2n + 1)$ , $b_2 = (n + 5)$ , and $h = (3n - 2)$ , which expression shows the correct application of the distributive property before simplification?
Maria is planning a rectangular vegetable garden where the length is 4 feet more than twice the width. She has 60 feet of fencing to enclose the garden. After setting up her equation $2w + 2(2w + 4) = 60$ where $w$ is the width, she solves and gets $w = 8.67$ feet. However, she realizes this creates practical problems for her garden layout. What should she consider doing next to make this more practical?

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