Lisa has only nickels and dimes in her money box. She knows that she has less than $15 in the box. Let x represent the number of nickels in the box and y represent the number of dimes in the box. Which of the following statements best describes the steps to graph the solution to the inequality in x and y?

Question

anonymous · Answer

Draw a dashed line to represent the graph of 5x + 10y = 1500, and shade the portion below the line for positive values of x and y.

 Draw a dashed line to represent the graph of 5x + 10y = 1500, and shade the portion above the line for positive values of x and y.

 Draw a dashed line to represent the graph of 10x + 5y = 1500, and shade the portion above the line for positive values of x and y.

 Draw a dashed line to represent the graph of 10x – 5y = 1500, and shade the portion below the line for positive values of x and y.

anonymous · Answer

@IMStuck 
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imstuck · Answer

I'm here to help! Since x represents nickels, the expression is either .05x or 5x. Since y represents dimes, the expression is either .10y or 10y. They either = 15 or 1500, depending upon which value you use (the decimal value or the value multiplied by 100 to get rid of the decimals.) So we have 5x + 10 y < 1500 because there is less than $15 in her bank or wherever she is keeping it. Now I suggest solving the equation for y just to see what kind of line it is. When you do that you get $$5x+10y <1500$$Move the 5x over and see that it is a negative number so the slope is negative.$$10y <-5x+1500$$Divide everything by 10 to get$$y <-\frac{ 1 }{ 2 }x +150$$The y-intercept is way up at 150 and it goes down one for every two it moves to the right. The point at the origin (0, 0) lies below the line and the point (1, 200) lies above the line. This point I just picked by looking at a very rough sketch of the graph. Test both points in the inequality now. Test (0, 0) first and see if it is true.$$5x+10y <1500-->5(0)+10(0)<1500?$$Yes it does work for the point (0, 0). Just to be sure, let's test the other point (1, 200).$$5(1)+10(200)<1500-->5+2000<1500?$$No it does not make the inequality true, so the answer would be the first choice you are given.