how to find the numbers in a word problem

Question

Burgers are 1.50 and drinks are 2.00 but i can't spend no more than $12. How would i right this inequality

Answer 1

write equation for the inequality 1.5 x + 2y = 12.

Step:- 1

Rewrite  equation in slope intercept form y = mx + b.

Where m is slope and b is y - intercept.

1.5 x + 2y = 12

Subtract 1.5x from each side.

2y = - 1.5 x +12

Divide each side by 2.

2y/2 = (- 1.5 x +12)/2

y = - 3/4x + 6

Step:- 2

The y - intercept is the value of  y when x = 0.

 y = - 3/4 (0) + 6                                                            (Substitute 0 for x )

y = 6

The y - intercept  is 6. The graph crosses the y - axis at (0, 6).

The x - intercept is the value of x when y = 0.

0 = - 3/4x + 6                                                                (Substitute 0 for y )

Subtract 6 from each side.

-6 = -3/4 x +6 -6

x = 8

The x - intercept  is 8. The graph crosses the y - axis at (8, 0).

Step:- 3

Use  these  ordered  pairs to graph the equation.

1. Draw  a coordinate plane

2. plot  the points

3. Draw a line through these points

4. The ordered  pairs on the line are solutions to the equation.

 

 

Answer 2

The inequality is 1.5x + 2y ≤ 12.                 (From the given data)

Rewrite the inequality in slope - intercept - form  y = mx + c, where m is slope and b is y - intercept.

2y ≤ 12 - 1.5x

y ≤ (- 1.5/2)x + 6.

Graph of the inequality :

The graph of the inequality y ≤ (- 1.5/2)x + 6 symbol is ≤, the boundary is included in the solution set.

Graph the boundary of the inequality y = (- 1.5/2)x + 6 with solid line.

• Draw the coordinate plane.
• To determine which half - plane to be shaded use a test point in either half - plane.

A simple choice is (0, 0).

Substitute x = 0 and y = 0 in the inequality y ≤ (- 1.5/2)x + 6.

0 ≤ (- 1.5/2)(0) + 6

0 ≤ 6.

The above statement is true.

• Since the statement is true, shade the region contains the point (0, 0).

Comments

The word " no more than " means that " less than or equal " and its inequality symbol is " ≤ ".

Let x be the number of the burgers and y be the number of drinks.

The cost of single burger is 1.50 dollars  and the cost of the single drink is 2.00 dollars.

The cost of x burger is 1.5x  and the cost of y drink is 2y dollars.

The total cost is 1.5x + 2y.

The total cost no more than $12 ⇒ 1.5x + 2y ≤ 12.

The inequality is 1.5x + 2y ≤ 12.