10. Linear Equations and Inequalities

A technician needs to prepare a disinfectant by mixing a 70% isopropyl alcohol solution with some 50% solution to obtain 65% alcohol. If the technician uses 500 mL of the 50% solution, how many mL of the 70% solution must be added?

Elena has \$18,500 to invest. She invests some of it at 8.4% annual simple interest for 1 year, and the remainder at 11.6% annual simple interest for 8 months. At the end of the year, her total interest earned is \$1,500. How much did she invest at each rate?

Maya needs 48 sq ft of tile for a backsplash. Basic tiles cost \$9 per sq ft and designer tiles cost \$25 per sq ft. She wants the overall average cost to be \$14 per sq ft. How many square feet of each tile should she use?

Mia has a jar containing nickels and dimes worth \$4.80 in total. If she has 12 more dimes than nickels, how many of each coin does she have?

A candy maker has 300mL of a 45% sugar syrup. She wants to dilute it with pure water to make a 30% syrup. How many mL of water should she add?

A retirement fund invests some money in government bonds at 2.5% annual simple interest, and \$5,000 more than that amount in corporate bonds at 4%. If the total annual interest earned is \$1,450, how much was invested in each type of bond?