if B=\$5 bills and T=\$20 bills, then 5B+20T=75   There are only 3 possible combinations, which are defined by the number of \$20 bills, those possibilities are:   1) When there is 1 \$20 bill: T=1 and B=11. Then: 5(11)+20(1)=75  That is, 11 \$5 bills and 1 \$20...

Let's start with the basic fact: perimeter is the sum of all sides: P=2W+2L     The perimeter of our rectangle is 50: P=50 The length of our rectangle is 3 times the width plus 1: L=3W+1   Now rewrite the first equation, substituting the...

I tried this approach: Luis wins the match if he wins the games as follows: 1,2,3 2,3,4 3,4,5 We don't consider games 4,5,6 because if the first game Luis wins is game 4, it means he lost the first 3; he's out. If Luis doesn't win 3 consecutive games, he needs to win 4 games...

If you want to use the Rational Zeros Theorem, as instructed, you need to use synthetic division to find zeros until you get a quadratic remainder.   P: ±1, ±2, ±3, ±6  (all prime factors of constant term) Q: ±1, ±7             ...

This is a classic.  I love it!    The problem's question is: "how many seconds does it take..." That's "time".  How are time, speed and distance related?   d = r x t  distance is equal to rate of speed multiplied by time.  Thus...

The problem states, in other words, that the mass of the sun is about 26 million times larger than the mass of the moon.  Therefore, if we know what the mass of the moon is, we just need to multiply it by 26 million and that will give us the mass of the sun:   Mass of the sun =...

Interesting problem, Hunter.  Let's figure it out!   I assume you're familiar with the basic of parabolas. Am I right?  OK.  Then, let's proceed...   How do we place the bridge at the coordinate plane?   Well, let's place one point at (0, 979)...

Amanda, you will find a lot of this type of word problems in your high school years and beyond.  A practical way to approach them is this:   Note that you have 2 categories: one is the number of items - two is the cost of the items. Set an equation for each:   1) The...

Since x = 4 is the vertical line that passes through (4, 3), its perpendicular line must be the horizontal line that passes through the same point, that is y = 3.  You will understand this better if you draw the lines on the coordinate plane. Let me know if you would like a further explanation...

Two pairs of numbers comply with the given condition, as it is to expect, since every quadratic equation has two solutions (except when the vertex of its graph is on the x-axis).   Let's see:   Let the numbers be x and (x+1)  -  They could be x and (x-1) as...

Let's say that m represents the amount of money members pay for aerobic classes at the fitness center.  The cost of the aerobic classes for members is defined by this simple equation:  m = 6 + 3x That is, members will pay a \$6 fee to the fitness center, plus \$3 every time they...

Ben,   The monthly cost of at least \$89 and at most \$137, may be defined as:   89 ≤ C ≤ 137     Since C = 25 + 0.80(x - 60), we get this compound inequality to solve:   89 ≤ 25 + 0.80(x - 60) ≤ 137     (89...

Nicole,    A key ingredient of success at working with word problems is defining units correctly.  In this case, note that the cost corresponds to 2 years of service.  Also, the problem asks for the one-month fee.  Then, a good start would be saying: OK, the cost...

Hayna,   When factoring trinomials of the form ax2 + bx + c, the first test you run is common factors.  Since there is none in this case, you should try factoring it by product of 2 binomials, or by the quadratic formula.   I wrote a simple program in...

Abby,   Distance = rate * time or (rate)(time) or "rate multiplied by time"   Define these values for each of the buses.  Let's call them bus 1 and bus 2:   Bus 1:  distance traveled: x miles           ...

If the pitch is 8, it means the roof raises 8 ft. per each horizontal 12 ft.  Since slope, m, is defined as the rise/run; then m = 8/12.   Simplifying, we obtain a slope m = 2/3 In order to write the line of the roof as an equation, let's assume that the roof line starts at...

There is a correlation between the measurement of the angles of a triangle and the length of their opposite sides: If the triangle is equiangular, then it is also equilateral If the triangle is isosceles, then at least two sides are congruent If the triangle does not have congruent...

I retract my opinion.  Byron, you're right.  Please accept my apology.

OK Joana, let's say that the amount Nico invested at 6% is x; and the amount at 5% is y.  Remember, % means percent, or "out of one hundred".  So 6% means 6/100; or \$6 per every \$100 invested.   If the two investments combined produced \$214, then we can set up an...

Hi Taryn.   To figure out if Marietta sold more cheese on Monday than on Tuesday, we need to compare the amount of cheese she sold on both days.  However, comparing 7/9 with 0.85 is like comparing cheese with butter: they both come from milk, but are different stuff.  In order...