The equation 3x+1.5y = 30 describes the number of burgers and hot dogs a family can buy with $30. What are the intercepts of the equation, and what does each represent?

3 Answers
Jun 27, 2018

Basically the intercepts represent the number of one of the items you can buy using the entire amount of $30.

Explanation:

Have a look:
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Jun 27, 2018

See a solution process below:

Explanation:

x-intercept: To find the x intercept set y to 0 and solve for x:

3x + (1.5 xx 0) = 30

3x + 0 = 30

3x = 30

(3x)/color(red)(3) = 30/color(red)(3)

(color(red)(cancel(color(black)(3)))x)/cancel(color(red)(3)) = 10

x = 10 or (10, 0)

y-intercept: To find the y intercept set x to 0 and solve for x:

(3 xx 0) + 1.5y = 30

0 + 1.5y = 30

1.5y = 30

(1.5y)/color(red)(1.5) = 30/color(red)(1.5)

(color(red)(cancel(color(black)(1.5)))y)/cancel(color(red)(1.5)) = 20

y = 20 or (0, 20)

The intercepts represent the maximum number of hotdogs or hamburgers the family could by,

So for example, if they bought no hotdogs (the y value equal to 0) they could buy 10 hamburgers, the x-intercept.

Jun 27, 2018

x intercept represents 10 burgers only can be bought in $30 , y intercept represents 20 hot dogs only can be bought in $30

Explanation:

3 x+ 1.5 y=30

Let x be the number of burgers of $3 cost per unit

and y be the number of hot dogs of $1.5 cost per unit

x intercept is found by putting y=0 in the equation.

3 x +1.5*0=30 or 3 x = 30 or x= 10 , It reveals that

10 burgers alone can be bought in $30

y intercept is found by putting x=0 in the equation.

3*0 +1.5 y=30 or 1.5 y = 30 or y= 30/1.5=20 , It reveals

that 20 hot dogs alone can be bought in $30

x intercept represent 10 burgers only can be bought in $30

y intercept represent 20 hot dogs only can be bought in $30

graph{3 x+1.5 y=30 [-80, 80, -40, 40]} [Ans]

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