Question

MS. Kitts works at a music store. Last week she sold 6 more than 3 times the number of CDs that she sold this week. Ms. Kitts sold a total of 110 CDs over the 2 weeks. Which system of equations can be used to find x, the number of CDs she sold last week, and y, the number of CDs she sold this week?

Answer 1

x - 3y = 6 and x + y = 110 represents the system of equations used to find x, the number of CDs she sold last week, and y, the number of CDs she sold this week

number of CDs Kitts sold last week "x" is 84 and number of CDs she sold this week "y" is 26

Solution:

Let "x" be the number of CDs Kitts sold last week

Let "y" be the number of CDs she sold this week

Given that Last week she sold 6 more than 3 times the number of CDs that she sold this week

Number of CDs Kitts sold last week = 6 + 3(number of CDs that she sold this week)

x = 6 + 3y ----- eqn 1

x - 3y = 6 ------- eqn 2

Given that Ms. Kitts sold a total of 110 CDs over the 2 weeks

Number of CDs Kitts sold last week + number of CDs she sold this week = 110

x + y = 110 ----- eqn 3

Thus eqn 2 and eqn 3 represents the system of equations used to find x, the number of CDs she sold last week, and y, the number of CDs she sold this week

Let us solve the above equations to find values of "x" and "y"

Substitute eqn 1 in eqn 3

6 + 3y + y = 110

6 + 4y = 110

4y = 104

y = 26

From eqn 3,

x + 26 = 110

x = 110 - 26 = 84

x = 84

Thus number of CDs Kitts sold last week = x = 84

Number of CDs she sold this week = y = 26