SOLUTION: The total expenditure E of a household is partly constant and partly varies directly as the size S of the household. (a) find the equation connecting E and S, if when E=300,S=5per

Algebra.Com
Question 1196618: The total expenditure E of a household is partly constant and partly varies directly as the size S of the household.
(a) find the equation connecting E and S, if when E=300,S=5persons and E=400,S=6
(b) what is the total expenditure when the size of the household is 10persoms
(c) how many persons will consume a total expenditure of $600
Found 2 solutions by MathLover1, MathTherapy:
Answer by MathLover1(20849)   (Show Source): You can put this solution on YOUR website!
if the total expenditure of a household is partly constant and partly varies directly as the size of the household, we have

were is a constant and the number of persons

a) find the equation connecting and , if when

, persons

.................solve for
...........eq.1


and,
.................solve for
...........eq.2

then from eq.1 and eq.2 we have

..............solve for



go to
...........eq.2, substitute




and equation is



b.
if

the total expenditure is $ when the size of the household is persons

c.
= $

........divide by


persons will consume a total expenditure of $

Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!

The total expenditure E of a household is partly constant and partly varies directly as the size S of the household.
(a) find the equation connecting E and S, if when E=300,S=5persons and E=400,S=6
(b) what is the total expenditure when the size of the household is 10persoms
(c) how many persons will consume a total expenditure of $600
This is a LINEAR system.

Let slope be m, and constant, b
We then get: E = mS + b____300 = 5m + b ----- eq (i)
             E = mS + b____400 = 6m + b ----- eq (ii) 
                           100 = m ----- Subtracting eq (i) from eq (ii)
                           300 = 5(100) + b ---- Substituting 100 for m in eq (i)
                     300 - 500 = b____- 200 = b

   Linear equation: E = mS + b______E = 100S - 200
                                    E = 100(10) - 200 --- Substituting 10 for S
For 10 people, expenditure or E = 1,000 - 200 = $800

   Linear equation: E = mS + b______E = 100S - 200
                                  600 = 100S - 200 ------ Substituting 600 for E
                            600 + 200 = 100S
                                  800 = 100S
Number of persons when expenditure is $600 or

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