Question

A new toy hits the local store. Sales (in hundreds) increase at a steady rate for several months, then decrease at about the same rate. This can be modeled by the function S(m)=-0.625\left|\mathrm{m}-8\right|+5S(m)=−0.625∣m−8∣+5 In what month(s) were 400 toys sold? A) 7th and 10th B) 5th C) 5th and 11th D) 4th and 12th

Answer 1

The month(s) when 400 toys were sold are the 7th month (-624) and the 10th month (640).

Step-by-step explanation:

To find the month(s) when 400 toys were sold, we need to solve the equation S(m) = 400. The equation S(m) = -0.625|m-8|+5 represents the toy sales, where m is the month.

Plug in S(m) = 400 into the equation:

400 = -0.625|m-8|+5

Subtract 5 from both sides:

400 - 5 = -0.625|m-8|

395 = -0.625|m-8|

Divide both sides by -0.625:

-632 = m-8 or 632 = m-8

Add 8 to both sides:

-632 + 8 = m or 632 + 8 = m

m = -624 or m = 640

The month(s) when 400 toys were sold are the 7th month (-624) and the 10th month (640).

Answer 2

Option A.

Step-by-step explanation:

It is given that, sales (in hundreds) for several months can be modeled by the function:

`S(m)=-0.625|m-8|+5`

We need to find the month in which 400 toys were sold.

Substitute S(m)=4 in the given function.

`4=-0.625|m-8|+5`

`4-5=-0.625|m-8|`

`-1=-0.625|m-8|`

`(-1)/(-0.625)=|m-8|`

`1.6=|m-8|`

Now,

`\pm 1.6=m-8`

`1.6=m-8` or
`-1.6=m-8`

`1.6+8=m` or
`-1.6+8=m`

`9.6=m` or
`6.4=m`

Approx the value to the next whole number.

`m\approx 10` or
`m\approx 7`

It means, 400 toys were sold on 7th and 10th month.

Therefore, the correct option is A.