Variables in Context - ISEE Upper Level: Quantitative Reasoning
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What does the variable $g$ represent if $m = 0.001g$ converts mass $m$ in kilograms from grams $g$?
What does the variable $g$ represent if $m = 0.001g$ converts mass $m$ in kilograms from grams $g$?
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$g$ is the mass in grams. The conversion multiplies $g$ by 0.001 to obtain kilograms, indicating it as the gram measurement.
$g$ is the mass in grams. The conversion multiplies $g$ by 0.001 to obtain kilograms, indicating it as the gram measurement.
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What does the variable $n$ represent if $S = 3n + 20$ is total savings $S$ after $n$ weeks saving $3$ dollars per week?
What does the variable $n$ represent if $S = 3n + 20$ is total savings $S$ after $n$ weeks saving $3$ dollars per week?
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$n$ is the number of weeks of saving. The savings model adds weekly amounts over $n$ periods to an initial sum, signifying $n$ as the time frame.
$n$ is the number of weeks of saving. The savings model adds weekly amounts over $n$ periods to an initial sum, signifying $n$ as the time frame.
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What does the variable $x$ represent if $A = x(x + 4)$ is the area of a rectangle with sides $x$ and $x + 4$?
What does the variable $x$ represent if $A = x(x + 4)$ is the area of a rectangle with sides $x$ and $x + 4$?
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$x$ is the length of the shorter side of the rectangle. The area formula uses $x$ as one side and multiplies by $x+4$, defining it as the smaller dimension.
$x$ is the length of the shorter side of the rectangle. The area formula uses $x$ as one side and multiplies by $x+4$, defining it as the smaller dimension.
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What does the expression $x + 4$ represent if a rectangle has side lengths $x$ and $x + 4$?
What does the expression $x + 4$ represent if a rectangle has side lengths $x$ and $x + 4$?
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$x + 4$ is the length of the longer side (4 units more than $x$). The expression adds 4 to the shorter side $x$ to define the adjacent longer side in the rectangle.
$x + 4$ is the length of the longer side (4 units more than $x$). The expression adds 4 to the shorter side $x$ to define the adjacent longer side in the rectangle.
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Identify the meaning of $x$ if $P = 2x + 2(x + 7)$ is the perimeter of a rectangle.
Identify the meaning of $x$ if $P = 2x + 2(x + 7)$ is the perimeter of a rectangle.
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$x$ is the length of the shorter side of the rectangle. The perimeter sums twice $x$ and twice $x+7$, indicating $x$ as the smaller side length.
$x$ is the length of the shorter side of the rectangle. The perimeter sums twice $x$ and twice $x+7$, indicating $x$ as the smaller side length.
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What does the variable $x$ represent if $y = 0.08x$ is the sales tax $y$ on a purchase amount $x$?
What does the variable $x$ represent if $y = 0.08x$ is the sales tax $y$ on a purchase amount $x$?
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$x$ is the pre-tax purchase price in dollars. The tax equation multiplies $x$ by 0.08, signifying it as the base amount before tax.
$x$ is the pre-tax purchase price in dollars. The tax equation multiplies $x$ by 0.08, signifying it as the base amount before tax.
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What does the variable $n$ represent if $T = 2.99n + 5.50$ is a bill with $n$ items plus a $5.50$ delivery fee?
What does the variable $n$ represent if $T = 2.99n + 5.50$ is a bill with $n$ items plus a $5.50$ delivery fee?
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$n$ is the number of items ordered. The bill adds delivery to 2.99 times $n$, indicating $n$ as the quantity of items.
$n$ is the number of items ordered. The bill adds delivery to 2.99 times $n$, indicating $n$ as the quantity of items.
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Identify the meaning of $x$ if $y = 5x + 12$ models total dollars $y$ after buying $x$ items plus a $12$ fee.
Identify the meaning of $x$ if $y = 5x + 12$ models total dollars $y$ after buying $x$ items plus a $12$ fee.
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$x$ is the number of items purchased. The equation adds a fixed fee to 5 times $x$ for total cost, showing $x$ as the variable quantity bought.
$x$ is the number of items purchased. The equation adds a fixed fee to 5 times $x$ for total cost, showing $x$ as the variable quantity bought.
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What does the variable $t$ represent if $d = 60t$ gives distance $d$ in miles traveled at $60$ mph?
What does the variable $t$ represent if $d = 60t$ gives distance $d$ in miles traveled at $60$ mph?
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$t$ is the time traveled in hours. The equation multiplies $t$ by speed to find distance, signifying it as the duration of travel.
$t$ is the time traveled in hours. The equation multiplies $t$ by speed to find distance, signifying it as the duration of travel.
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What does the variable $x$ represent if $C = 2.50x$ is the total cost in dollars for $x$ movie tickets?
What does the variable $x$ represent if $C = 2.50x$ is the total cost in dollars for $x$ movie tickets?
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$x$ is the number of movie tickets purchased. The equation multiplies $x$ by the price per ticket to compute total cost, indicating it as the quantity purchased.
$x$ is the number of movie tickets purchased. The equation multiplies $x$ by the price per ticket to compute total cost, indicating it as the quantity purchased.
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Identify the meaning of $12$ in $y = 5x + 12$ if $y$ is total cost and $x$ is number of items.
Identify the meaning of $12$ in $y = 5x + 12$ if $y$ is total cost and $x$ is number of items.
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$12$ is the fixed fee (cost when $x = 0$). As the $y$-intercept, 12 represents the constant cost incurred even when no items are purchased.
$12$ is the fixed fee (cost when $x = 0$). As the $y$-intercept, 12 represents the constant cost incurred even when no items are purchased.
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What does the variable $b$ represent if $y = mx + b$ models total cost $y$ with units $x$ purchased?
What does the variable $b$ represent if $y = mx + b$ models total cost $y$ with units $x$ purchased?
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$b$ is the fixed starting amount (the value when $x = 0$). The $y$-intercept $b$ in the equation indicates the initial value of $y$ when no units are purchased.
$b$ is the fixed starting amount (the value when $x = 0$). The $y$-intercept $b$ in the equation indicates the initial value of $y$ when no units are purchased.
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What does the variable $m$ represent if $y = mx + b$ models cost $y$ with a fixed fee $b$ and per-unit rate $m$?
What does the variable $m$ represent if $y = mx + b$ models cost $y$ with a fixed fee $b$ and per-unit rate $m$?
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$m$ is the per-unit rate (change in $y$ per $1$ unit of $x$). In the linear model, $m$ represents the constant rate of change in $y$ for each unit increase in $x$.
$m$ is the per-unit rate (change in $y$ per $1$ unit of $x$). In the linear model, $m$ represents the constant rate of change in $y$ for each unit increase in $x$.
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What does the variable $t$ represent if $I = prt$ gives simple interest $I$ at rate $r$?
What does the variable $t$ represent if $I = prt$ gives simple interest $I$ at rate $r$?
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$t$ is the time the money is invested or borrowed (in years). The formula uses $t$ to scale interest accumulation, measured in years for the investment period.
$t$ is the time the money is invested or borrowed (in years). The formula uses $t$ to scale interest accumulation, measured in years for the investment period.
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What does the variable $r$ represent if $I = prt$ gives simple interest $I$ over time $t$?
What does the variable $r$ represent if $I = prt$ gives simple interest $I$ over time $t$?
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$r$ is the annual interest rate (as a decimal). In the interest equation, $r$ scales the principal over time to calculate earnings, expressed as a decimal.
$r$ is the annual interest rate (as a decimal). In the interest equation, $r$ scales the principal over time to calculate earnings, expressed as a decimal.
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What does the variable $p$ represent if $I = prt$ is simple interest earned $I$ in dollars?
What does the variable $p$ represent if $I = prt$ is simple interest earned $I$ in dollars?
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$p$ is the principal (initial amount of money). The interest formula multiplies $p$ by rate and time, denoting it as the initial investment amount.
$p$ is the principal (initial amount of money). The interest formula multiplies $p$ by rate and time, denoting it as the initial investment amount.
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What does the variable $h$ represent if $V = lwh$ is the volume of a rectangular prism?
What does the variable $h$ represent if $V = lwh$ is the volume of a rectangular prism?
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$h$ is the height of the rectangular prism. In the volume formula, $h$ is one dimension multiplied with length and width to determine total space.
$h$ is the height of the rectangular prism. In the volume formula, $h$ is one dimension multiplied with length and width to determine total space.
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What does the variable $w$ represent if $C = 15w$ is pay $C$ in dollars for working $w$ hours at $15$ per hour?
What does the variable $w$ represent if $C = 15w$ is pay $C$ in dollars for working $w$ hours at $15$ per hour?
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$w$ is the number of hours worked. The pay equation multiplies $w$ by hourly rate, denoting it as the duration of labor.
$w$ is the number of hours worked. The pay equation multiplies $w$ by hourly rate, denoting it as the duration of labor.
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What does the variable $c$ represent if $F = rac{9}{5}c + 32$ converts Celsius $c$ to Fahrenheit $F$?
What does the variable $c$ represent if $F = rac{9}{5}c + 32$ converts Celsius $c$ to Fahrenheit $F$?
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$c$ is the temperature in degrees Celsius. The formula scales $c$ by $\frac{9}{5}$ and adds 32 to convert to Fahrenheit, marking it as Celsius input.
$c$ is the temperature in degrees Celsius. The formula scales $c$ by $\frac{9}{5}$ and adds 32 to convert to Fahrenheit, marking it as Celsius input.
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