Question

Chris put a total of $975 in two different investments, one that earned 5% interest and one that earned 12% interest. The total investment income was $111. If x represents the amount invested at 5% and y represents the amount invested at 12%, the system of linear equations that models the scenario is the following:
{x +y= 975
| 0.05x + 0.12y = 111
The graph is titled Investments. The letter x is to the right of the horizontal axis which is labeled from 0 to 500 in steps of 50. The label amount of money in dollars invested at 5% interest is below the graph.
The letter y is above the vertical axis which is labeled from 0 to 1,100 in steps of 100. The label amount of money in dollars invested at 12% interest is to the left of the graph. A red solid line passes through the approximate points left parenthesis 0 comma 975 right parenthesis, left parenthesis 85 comma 900 right parenthesis, and left parenthesis 450 comma 525 right parenthesis. The line is labeled x plus y equals 975. A blue dashed line passes through the approximate points left parenthesis 0 comma 925 right parenthesis, left parenthesis 85 comma 900 right parenthesis, and left parenthesis 450 comma 725 right parenthesis. The line is labeled 0.05 x plus 0.12 y equals 111.
Which point represents the best estimate to the solution of the system of linear equations?
(1 point)
The point that is the best estimate to the solution of the system of linear equations is ___
(880, 120)
(900, 85)
(120, 880)
(85, 900)

Answer 1

(85, 900)

Work check: x + y = 975 and 0.05x + 0.12y = 111 gives y ≈ 889.29, x ≈ 85.71, so (85, 900) is the best estimate from the choices.