Equation From a Situation - ISEE Middle Level Mathematics Achievement

1. Which equation models: You buy $x$ notebooks at $3 each and pay $2 tax; total cost is $T$?

   $T=3x+2$. Calculates total cost as the price per notebook times quantity plus fixed tax.

2. Which equation models: A car starts with $g$ gallons and uses $0.05$ gallons per mile for $x$ miles; remaining gas is $R$?

   $R=g-0.05x$. Subtracts the gas consumed at 0.05 gallons per mile from the initial amount.

3. Which equation models: The sum of two consecutive integers is $41$; let the first be $n$?

   $n+(n+1)=41$. Adds two consecutive integers to equal 41.

4. Which equation models: The sum of three consecutive integers is $72$; let the middle integer be $n$?

   $(n-1)+n+(n+1)=72$. Sums three consecutive integers with n as the middle to equal 72.

5. Which equation models: A rectangle has width $w$ and length $w+6$; its area is $84$ square units?

   $w(w+6)=84$. Sets the product of width and length (width plus 6) equal to the given area.

6. Which equation models: A gym charges $25 per month plus a $40 sign-up fee; total after $m$ months is $C$?

   $C=25m+40$. Adds the monthly fees for m months to the one-time sign-up fee.

7. Which equation models: The perimeter $P$ of a rectangle with length $l$ and width $w$?

   $P=2l+2w$. Computes the perimeter by adding twice the length and twice the width.

8. Which equation models: A taxi charges a $4 fee plus $2 per mile for $m$ miles, total cost $C$?

   $C=4+2m$. Represents the total cost as the fixed fee plus the per-mile charge times the number of miles.

9. Which equation models: The sum of angles in a triangle is $180^\circ$; if angles are $x$, $x$, and $y$, what equation relates them?

   $2x+y=180$. Sums twice one angle and the other angle to equal the total interior angles of a triangle.

10. Which equation models: You split $60 equally among $n$ friends; each friend gets $x$ dollars?

    $x=\frac{60}{n}$. Divides the total money by the number of friends to find each person's share.

11. Which equation models: You have $50 and spend $\$x$; remaining money is $R$?

    $R=50-x$. Calculates the remaining money by subtracting the amount spent from the initial $50.

12. Which equation models: The average of $a$, $b$, and $c$ is $M$?

    $M=\frac{a+b+c}{3}$. Computes the arithmetic mean by summing the values and dividing by 3.

13. Which equation models: A jacket originally costs $p$ dollars and is discounted by $20\%$; sale price is $S$?

    $S=0.8p$. Applies an 80% factor to the original price to account for the 20% discount.

14. Which equation models: The area $A$ of a triangle with base $b$ and height $h$?

    $A=\frac{1}{2}bh$. Determines the area by multiplying the base and height, then dividing by 2.

15. Which equation models: The number $y$ is $5$ more than one-third of $x$?

    $y=\frac{1}{3}x+5$. Adds 5 to one-third of x to obtain y.

16. Which equation models: The number $y$ is $12$ less than twice $x$?

    $y=2x-12$. Expresses y as twice x reduced by 12.

17. Which equation models: A recipe uses $\frac{3}{4}$ cup of sugar per batch; for $b$ batches, total sugar is $S$ cups?

    $S=\frac{3}{4}b$. Multiplies the sugar per batch by the number of batches to find total sugar needed.

18. Which equation models: A line has slope $3$ and $y$-intercept $-2$; what is its equation in slope-intercept form?

    $y=3x-2$. Applies the slope-intercept form $y=mx+b$ with slope 3 and y-intercept -2.

19. Which equation models: The number of minutes $m$ is $60$ times the number of hours $h$?

    $m=60h$. Converts hours to minutes by multiplying by 60.

20. Which equation models: The total cost $C$ for $n$ items at $8 each with a $5 coupon off the total?

    $C=8n-5$. Subtracts the coupon value from the total cost of n items at $8 each.

21. Which equation models: Three times a number $n$ decreased by $5$ is $19$?

    $3n-5=19$. Represents three times n minus 5 equaling 19.

22. Which equation models: The distance $d$ traveled at speed $r$ for time $t$?

    $d=rt$. Expresses distance as the product of rate and time.

23. Which equation models: A number $x$ increased by $7$ equals $15$?

    $x+7=15$. Models the situation where adding 7 to x results in 15.

24. Which equation models: You deposit $200 and then add $15 each week for $w$ weeks; total is $T$?

    $T=200+15w$. Adds the weekly additions for w weeks to the initial deposit.

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