Equivalent Equations

$P(c)=60c-35c-26$

$P(b)=1.25b-10$

1. A company sells both handmade stocking caps and mass produced beanies. The functions above show how much profit $P(c)$ they make on $c$ handmade stocking caps and how much profit $P(b)$ they make on $b$ beanies. The beanies are much cheaper to buy, but they also yield a much smaller profit. How many beanies do they have to sell to equal the profit from 25 handmade stockingcaps.

$C(m)=45+2.70(\dfrac{m}{20})$

$A(m)=300+.05m$

2. The functions above show the cost of a trip by car $C(m)$ and by airplane $A(m)$ based upon the miles $m$ of the trip. For a trip for which it would cost the same amount to fly or drive, how much would it cost to fly?

$A(x)=150+.55x$

$P(x)=230+.35x$

3. The functions above the cost of growing $x$ number of apples and $x$ number of pears. For the quantity of fruit for which it costs the same to grow apples or pears, how much does it cost to grow apples?

4. At a cafe, coffee costs \$1.25 a cup, and lattes cost twice as much as coffee. Donut holes are 35 cents each, and donuts are 90 cents. If a mom orders a latte and a donut, and tells her child he can spend the same amount of money (but no more), how many donut holes can he buy?

5.  A YMCA preschool charges a \$100 enrollment fee and \$795 a month in tuition. A local church preschool charges no enrollment fee but charges \$800 a month plus a 3% surcharge on that tuition each month. After how many months is it more cost efficient to attend the YMCA rather than the church preschool?