Variables in Context - ISEE Lower Level Quantitative Reasoning

1. What expression represents the number of cents in $d$ dollars?

   $100d$. Multiplying dollars d by 100 converts the amount to cents using the standard conversion rate.

2. What expression represents "$7$ less than twice a number $n$"?

   $2n - 7$. Multiplying n by 2 and then subtracting 7 captures twice the number reduced by 7.

3. What expression represents "the difference between $12$ and a number $p$"?

   $12 - p$. Subtracting p from 12 calculates the difference by removing p from the fixed value 12.

4. What expression represents "$4$ divided by $m$"?

   $\frac{4}{m}$. Dividing 4 by m represents the quotient when 4 is divided by the variable m.

5. What expression represents "$3$ more than half of a number $y$"?

   $\frac{y}{2} + 3$. Dividing y by 2 and adding 3 expresses a value 3 greater than half of y.

6. What expression represents "twice the sum of a number $x$ and $3$"?

   $2(x + 3)$. Multiplying the sum of x and 3 by 2 represents twice that combined quantity.

7. What equation represents: "A number $x$ increased by $9$ equals $20$"?

   $x + 9 = 20$. Setting x plus 9 equal to 20 models the situation where adding 9 to x results in 20.

8. What equation represents: "Three times a number $y$ minus $4$ is $11$"?

   $3y - 4 = 11$. Setting 3y minus 4 equal to 11 models three times y reduced by 4 equaling 11.

9. What expression represents your distance after traveling $t$ hours at $60$ miles per hour?

   $60t$. Multiplying time t by the constant speed of 60 yields the total distance traveled.

10. What expression represents the total cost for $n$ items at $4 each after a $3 discount?

    $4n - 3$. Multiplying n by 4 and subtracting 3 reflects the item costs reduced by the discount.

11. What expression represents "triple the number of seats $s$, then add $5$"?

    $3s + 5$. Multiplying s by 3 and adding 5 combines tripling the seats with an additional 5.

12. What expression represents the area of a rectangle with length $L$ and width $W$?

    $LW$. Multiplying length by width calculates the area enclosed by the rectangle.

13. What expression represents the average of two numbers $a$ and $b$?

    $\frac{a + b}{2}$. Summing a and b then dividing by 2 computes the mean value between them.

14. What does the expression $x + 5$ represent if $x$ is a number of stickers and $5$ more are added?

    The total number of stickers after adding $5$. Adding 5 to the variable x, which represents the initial number of stickers, gives the total after the addition.

15. What expression represents the perimeter of a rectangle with length $L$ and width $W$?

    $2L + 2W$. Adding twice the length and twice the width gives the total perimeter of the rectangle.

16. What expression represents "$4$ times as many as $m$"?

    $4m$. Multiplying m by 4 expresses a quantity four times larger than m.

17. What expression represents "$5$ fewer than triple a number $t$"?

    $3t - 5$. Multiplying t by 3 and subtracting 5 expresses a value 5 less than three times t.

18. What expression represents "$m$ divided by $4$"?

    $\frac{m}{4}$. Dividing m by 4 represents splitting m into four equal parts.

19. What expression represents "the sum of twice a number $x$ and $3$"?

    $2x + 3$. Adding 3 to twice x represents the sum of those terms.

20. What expression represents "$7$ less than a number $n$"?

    $n - 7$. Subtracting 7 from n expresses a value that is 7 less than the original number.

21. What expression represents the number of minutes in $h$ hours?

    $60h$. Multiplying hours h by 60 converts the time to minutes using the fixed rate per hour.

22. What expression represents "half of the quantity $y$ plus $3$"?

    $\frac{y + 3}{2}$. Dividing the sum of y and 3 by 2 represents half of that total quantity.

23. What expression represents "the difference between a number $p$ and $12$"?

    $p - 12$. Subtracting 12 from p calculates the difference by removing 12 from the larger value p.

24. What expression represents the total cost for $n$ items at $4 each plus a $3 fee?

    $4n + 3$. Multiplying n by 4 and adding 3 accounts for the cost per item plus the fixed fee.

25. What expression represents "the product of $9$ and a number $k$ decreased by $4$"?

    $9k - 4$. Multiplying k by 9 and subtracting 4 decreases the product by 4.

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