Question

Tania has 56 liters of milk. She uses the milk to make muffins and cakes. Each batch of muffin requires 7 liters of milk and each batch of cakes require 4 liters of milk. Let x be the number of batches of muffins and y be the number of batches of cakes that Tania can make. Which of the following graphs best shows all the possible number of batches of muffins and cakes that Tania can make? Line joining ordered pairs 0, 8 and 6, 3.5. Shade the portion of the graph below this line which lies within the first quadrant Line joining ordered pairs 0, 8 and 6, 3.5. Shade the portion of the graph above this line which lies within the first quadrant Line joining ordered pairs 0, 14 and 8, 0. Shade the portion of the graph above this line which lies within the first quadrant Line joining ordered pairs 0, 14 and 8, 0. Shade the portion of the graph below this line which lies within the first quadrant

Answer 1

Write the inequalities that are given by the :

x: the number of batches of muffins

y: the number of batches of cakes

Each batch of muffin requires 7 liters of milk and each batch of cakes require 4 liters of milk.

=> liters of milk use = 7x  + 4y

Tania has 56 liters of milk.=> 7x + 4y ≤ 56

Which means that the amount of muffins and cakes made are limited by the availability of 56 liter of milk.

The inequality 7x + 4y ≤ 56 is graphed by drawing the line 7x + 4y = 56 and shading the region below that line.

The line 7x + 4y = 56 has these x and y intercepts:

y-intercept: x =0 => 4y = 56 => y = 56/4 => 14 => point (0,14)

x-intercept => y = 0 => 7x = 56 => x = 56/7= 8  => point (8,0)

So, the line passes through the poins (0,8) and (14,0) and the solution region is below that line.

Also, you know that x and y are restricted to be positive or zero =>

x ≥ 0

y ≥ 0.

So, the solution region is restricted to the first quadrant.

That implies that the answer is:

Line joining ordered pairs 0, 14 and 8, 0. Shade the portion of the graph below this line which lies within the first quadrant