Write the word or phrase that best completes each statement or answers the question.
-A store sells televisions for $360 and digital video recorders for $270. At the beginning of the week its entire stock is worth $59,580. During the week it sells three quarters of the televisions and one
Third of the digital video recorders for a total of $34,560. How many televisions and digital video
Recorders did it have in its stock at the beginning of the week?
A) 95 televisions; 94 digital video recorders
B) 98 televisions; 90 digital video recorders
C) 96 televisions; 96 digital video recorders
D) 97 televisions; 93 digital video recorders

Question

Quizplus · Accepted Answer

Let the number of televisions be $T$ and the number of digital video recorders be $D$. The total value of the stock is given by $360T + 270D = 59580$. The value of the items sold is $34,560$, which comes from selling $3/4$ of the televisions and $1/3$ of the digital video recorders, so the equation for the sales is $270(360T(3/4) + 270D(1/3)) = 34560$. Solving these equations simultaneously gives $T = 98$ and $D = 90$, making option B correct.

Write the Word or Phrase That Best Completes Each Statement