6th Grade Math - Foster 223-1931-99913
Johnny works on Bob's Burger Barn and makes
$8.10 an hour. He works 9 1/2 hours each week.
He is saving his money to buy a Nintendo Switch
which costs $299.99. How many weeks must
Johnny work before he can purchase the game?
About how many hours must he work?
Dar Forter. 1247 PM
Explain your are
Due 11-59

4 weeks

38 hours

Step-by-step explanation:

First determine how much he makes each week

8.10 * 9.5 =76.95 per week

Multiply this by w  to determine the amount he will make in w weeks

76.95w

This must be greater than or equal to the amount he needs

76.95w ≥299.99

Divide each side by 76.95

76.95w/76.95  ≥299.99/76.95

w≥3.89851

Rounding to a whole number of weeks

4 weeks

4 weeks at 9.5 hours =

4* 9.5 =38 hours

x -

median = 1.25

range = 12-14.5

interquartile = q12-q14.5

y -

median = 1

range = 15-17

interquartile = q15-q17

a) 40 more; b) old factory:   10%, new factory:   16%; c) week 4

explanation:

a) at week 0, we see in the graph that the new factory produces 190 specialty items.  

using the function, substituting 0 in for w,

this is a difference of 230-190 = 40.

b) the function for the old factory is written in the form f(x) = a(1+r)ˣ, where a is the original amount, x is the amount of time and r is the growth rate.   the equation for the old factory is ; 230 is in place of a and is the original amount; w is the amount of time; which means 1+r = 1.1.   this means that r must be 0.1 or 10%.

for the new factory, we find the percent of increase to find the growth rate; the formula for this is

between the first two points, the amount of change is 220-190 = 30; this gives us

30/190 = 0.158 ≈ 0.16 = 16%

c) at week 0, the old factory has 230 while the new factory has 190.

at week 1, the old factory has 230(1.1) = 253 while the new factory has 220.

at week 2, the old factory has 230(1.1²) = 278.3 while the new factory has 252.

at week 3, the old factory has 230(1.1³) = 306.13 while the new factory has 290.

at week 4, the old factory has 230(1.1⁴) = 336.743 while the new factory has 337.   this is the first week that the new factory surpasses the old.