If ~$a $~= 1+~$\frac{1}{4}$~+~$\frac{1}{16}$~ +~$\frac{1}{64}$~and ~$b$~=1+~$\frac{1}{4}$~a then what is the value of ~$a $~– ~$b$~?

Half of a large pizza is cut into 4 equal-sized pieces, and the other half is cut into 6 equal-sized pieces. If a person were to eat 1 of the large pieces and 2 of the smaller pieces, what fraction of the pizza would remain uneaten?

When a subscription to a new magazine was purchased for ~$m$~ months, the publisher offered a discount of 75 percent off the regular monthly price of the magazine.If the total value of the discount was equivalent to buying the magazine at its regular monthly price for 27 months, what was the value of ~$m$~?

Each machine at a toy factory assembles a certain kind of toy at a constant rate of one toy every 3 minutes. If 40 percent of the machines at the factory are to be replaced by new machines that assemble this kind of toy at a constant rate of one toy every 2 minutes, what will be the percent increase in the number of toys assembled in one hour by all the machines at the factory, working at their constant rates?

 Judy bought a quantity of pens in packages of 5 for $0.80 per package. She sold all of the pens in packages of 3 for $0.60 per package. If Judy’s profit from the pens was $8.00, how many pens did she buy and sell?

A school club plans to package and selldried fruit to raise money. The club purchased 12 containers of dried fruit,each containing 16~$\frac{3}{4}$~ pounds. What is the maximum number of individual bags of driedfruit, each containing ~$\frac{1}{4}$~ pounds, that can be sold from the dried fruitthe club purchased?

 How many integers between 1 and 16, inclusive, have exactly 3 different positive integer factors? (Note: 6 is NOT such an integer because 6 has 4 different positive integer factors: 1, 2, 3, and 6. )

 Howmany integers ~$x$~ satisfy both 2<~$x$~≤4and 0≤~$x$~≤3?

If ~$x-y$~ = ~$R$~ and ~$xy $~ = ~$S$~ , then ~$(x-2) (y+2)$~ =

As shown in the diagram above. a lever resting on a fulcrum has weights of ~$w_1$~ pounds and  ~$w_2$~ pounds, located ~$d_1$~ feet and ~$d_2$~ feet from the fulcrum. The lever is balanced and ~$w_1d_1=w_2d_2$~ . Suppose ~$w_1$~ is 50 pounds and ~$w_2$~ is 30 pounds. If ~$d_1$~ is 4 feet less than ~$d_2$~ ,what is ~$d_2$~, in feet?