Algebra Assement

Question

1. 1. You have $150 to spend at a store. If you shoes cost $30 and belts cost $25, write an equation that represents the different ways that you could spend a total of $150.
2. 2. Create a graph of the equation from question 1.
3. 3. A swimming pool is being drained at a constant rate of 3 inches (depth of the water) per hour. The depth of the water after 5 hours is 32 inches. Write the equation for this function in point slope form.
4. 4. Graph your function to find how long it will take to empty the pool completely

Answer 1

shoes cost $30

belts cost $25

$150 to spend

30s + 25b = 150

6s + 5b = 30

you can buy 5 shoes and no belts

or 6 belts and no shoes

or 1 shoes, 4 belts and $4 left over

2 shoes 3 belts and $3 left over

3 shoes 2 belts and $2 left over

4 shoes 1 belt and $1 left over

let x= s, y = b, then 6x +5y = 30

5y = -6x +30

y = -6x/5 + 6, graphically it has slope =-6/5 =-1.2 and y intercept =6

plot the intercept points (0,6) and (5,0) draw a line through them, that's the graph of the equation

pool drains at 3 inches per hour. after 5 hours 32 inches= depth of the water in the pool

d(h) = F - 3h where F = depth when Full, h= hours, d=depth after h hours

32 = F -3(5)

F = 32+15 =47 inches when Full

d = 47-3h

pool will be empty when d= 0 = 47-3h

3h =47

h = 47/3 = 15 2/3 hours

d=47-3h is graphically a straight line with slope = -3 and y intercept = 47