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Answers by Gene G.

Word Problem (answer)

a = hours in office b = hours driving tractor   First statement - Her total pay is: 10a + 12b = 416 Second statement - hours worked: a = 2b   Substitute 2b for a in the first equation: 10(2b) + 12b = 416 20b + 12b = 416 32b = 416 b...

Story Problem (answer)

Look for ways to break word problems into pieces, then handle them one at a time to build an equation.   First, find what the manufacturer charges the store chain. cost to store: m+4 The store then charges 170% of its cost.  170%=1.7 Selling price is cost times...

5t[t-(r-s)] (answer)

This is just an order of operations question.  PEMDAS 5t[t-(r-s)] Start with the inner-most parentheses: 5t[t-r+s]      you can think of -(r-s) as (-1)(r-s) Now expand the remaining expression: (5t)(t) - (5t)(r) + (5t)(s) 5t2-5rt+...

You can write two equations from the problem statement. First assign variable names for the coins d = the number of 10-cent coins (dimes) n = the number of 5-cent coins (nickels) The easy equation comes from the first statement.  You can calculate the total value of the coins: 0...

A more direct approach.   Let l be the dimension parallel to the barn's wall. l + 2w = 100   Total length of fencing used.  Notice there's only one l. l = 100 - 2w   A =  lw = (100-2w)(w) = -2w2+100w This parabola describes area versus...

"Grade" is most often seen in situations where it refers to the slope of the ground.  A highway sign warning for a steep hill may reference a 10% grade.  You can also snoop around for home building or landscaping applications where it may be referenced as inches per foot. ...

Solve for x, a/x+a + b/x-b = (a+b)/(x+c)   This one is a bit too messy to type out without a real equation editor, but here's how to proceed.   (I assumed that the x+a and x-b should have been in parentheses.)   Find a common denominator...

Here's the hard way: Starting with A: A    AB       ABC       ABD       ABE    AC       ACD       ACE    AD       ADE B   ...

Finding quartile (answer)

Put your numbers in order (27, 27, 57, 57, 59, ...) Divide them into 4 same-sized groups. There are 24 numbers in the dataset, so it divides into 4 groups with 6 values in each one.   Since the dividing lines between fourths (quarters) all lie between two numbers (for...

"Similar" means one is a scale model of the other.   If you increase all dimensions of ANY plane figure by a factor, the ratio of the areas is that factor squared!   Large dimension is 4x the small one. The ratio is 16:1.   Try it with a couple...

Pr(T) would be the probability of getting tails. The probability of getting heads OR tails is 100%, or 1.0, so Pr(H) = 1.0 - 0.6 = 0.4. That's 4 out of 10.   How many heads out of 85 tosses? 0.4 * 85 = 34