MA141 Grantham Linear Equation and Equilibrium Point Problems Paper I just need help with these questions. And please explain how you got the answers. 1) Y

MA141 Grantham Linear Equation and Equilibrium Point Problems Paper I just need help with these questions. And please explain how you got the answers. 1) You receive two job offers. One offers a straight commission of 6% of sales. The other offers a salary
of $500 per week plus 3% of sales. How much would you have to sell per week
in order for the straight commission job offer to be better?
2) Five hundred gallons of 89-octane gasoline is obtained by mixing 87-octane gasoline with 92-octane
gasoline. (a) Write a system of equations in which one equation represents the total amount of final
mixture required and the other represents the amounts of 87- and 92-octane gasoline in the final
mixture. Let x and y represent the numbers of gallons of 87- and 92-octane gasoline, respectively. (b)
Use a graphing utility to graph the two equations in part (a) in the same viewing window. As the amount
of 87-octane gasoline increases, how does the amount of 92-octane gasoline change? (c) How much of
each type of gasoline is required to obtain the 500 gallons of 89-octane gasoline?
3) A total of $32,000 is invested in two municipal bonds that pay 5.75% and 6.25% simple interest. The
investor wants an annual interest income of $1900 from the investments. What amount should be
invested in the 5.75% bond?
4) A mixture of 5 pounds of fertilizer A, 13 pounds of fertilizer B, and 4 pounds of fertilizer C provides the
optimal nutrients for a plant. Commercial brand X contains equal parts of fertilizer B and fertilizer C.
Commercial brand Y contains one part of fertilizer A and two parts of fertilizer B. Commercial brand Z
contains two parts of fertilizer A, five parts of fertilizer B, and two parts of fertilizer C. How much of each
fertilizer brand is needed to obtain the desired mixture?
5) A chemist needs 10 liters of a 25% acid solution. The solution is to be mixed from three solutions
whose concentrations are 10%, 20% and 50%. How many liters of each solution will satisfy each
condition?
a) Use 2 liters of the 50% solution.
b) Use as little as possible of the 50% solution.
c) Use as much as possible of the 50% solution.

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