A company packs raisins in 500 g cartons and 750 g bags. One day, 887.5 kg of raisins were packed into full cartons and bags. Ben wondered how many cartons and how many bags could have been packed. State the linear equation which represents this situation.

Milk is leaking from a carton at a rate of 4 mL/min. There is 1500 ml. of milk in the carton at 8:30 a.m.

a) Write an equation and draw a graph for this situation.

b) Use your equation to determine algebraically when 1 L of milk will be left in the carton.

Solve the system of equations.

\displaystyle \begin{array}{lllll} &3x + y = - 2 \\ &5x - y = - 10 \end{array}

Solve the system of equations.

\displaystyle \begin{array}{lllll} &2x + 7 = y \\ &-3x - 2y = 10 \end{array}

Solve the system of equations.

\displaystyle \begin{array}{lllll} &3x + 5y = -9 \\ &2x - y = 7 \end{array}

Sarah needs 20 g of 80% gold to make a pendant. She has some 85% gold and some 70% gold. from broken jewellery and wants to know how much of each she should use. Determine the quantity of each alloy that she should use.

Create two linear systems that are equivalent to the system

3x + 4y = - 8

x - 2y = 9

Min likes to go cycling. He cycles partly on payed surfaces and partly off-road. through hilly and wooded areas. He cycles at 25 km/h on paved surfaces and at 10 km/h off-road. One day he cycled 41 km in 2 h. How far did he cycle off-road?

Last summer, Betty earned $4200 by painting houses. She invested some of the money in a savings account that paid 3.5%/year and the rest in government bond that paid 4.5%/year. After one year, she has earned $174 in interest. How much did she invest at each rate?

Explain how you know that this system of equations has no solution.

\displaystyle \begin{array}{lllll} &15 -6y = 9x\\ &3x + 2y = 8 \end{array}