Q22. Select & Place the Correct Letter (A-D) Ted and Asanji each improved their yards by planting daylilies and ivy.They bought their supplies from the same store. Ted spent 92 on 4 daylilics and 12 pots of ivy. Asanji spent 99 on 3 daylilies and 14 pots of ivy. Find the cost of one daylily and the cost of one pot ofivy. A) daylily: 4 pot of ivy: 3 B) daylily: 4, pot of ivy: 9 C daylily: 6 pot of ivy: 5 D) daylily: 5, pot of ivy: 6 in Short Answer Response 4 poi

To solve this problem, we can set up a system of linear equations based on the given information.<br /><br />Let's denote the cost of one daylily as \( x \) and the cost of one pot of ivy as \( y \).<br /><br />From the given information, we can write the following equations:<br /><br />\[ 4x + 12y = 92 \] (Equation 1)<br />\[ 3x + 14y = 99 \] (Equation 2)<br /><br />Now, we can solve this system of equations to find the values of \( x \) and \( y \).<br /><br />First, let's multiply Equation 1 by 3 and Equation 2 by 4 to make the coefficients of \( x \) the same:<br /><br />\[ 12x + 36y = 276 \] (Equation 3)<br />\[ 12x + 56y = 396 \] (Equation 4)<br /><br />Next, we can subtract Equation 3 from Equation 4 to eliminate \( x \):<br /><br />\[ 20y = 120 \]<br /><br />Dividing both sides by 20, we get:<br /><br />\[ y = 6 \]<br /><br />Now that we have the value of \( y \), we can substitute it back into Equation 1 to find the value of \( x \):<br /><br />\[ 4x + 12(6) = 92 \]<br />\[ 4x + 72 = 92 \]<br />\[ 4x = 20 \]<br />\[ x = 5 \]<br /><br />Therefore, the cost of one daylily is $5 and the cost of one pot of ivy is $6.<br /><br />So, the correct answer is:<br />D) daylily: $5, pot of ivy: $6