Suppose that in one week, your company takes in $2,220 in sales at one of its ce

Question

Suppose that in one week, your company takes in $2,220 in sales at one of its cell phone stores. The price breakdown per phone is as follows:
Cell phone model A4: $35
Smartphone Z20: $50

Suppose that a total of 51 phones were sold.
a.Set up the system of equations that needs to be solved to determine how many of each type of phone were sold. Give a clear definition of the variables in the system.
b.Solve the system of equations, showing clearly how the solution was determined, and state the results clearly in light of the real-world situation.

Explanation / Answer

defining variables: x = the number of model A4 y = the number of model Z20 The two equations you have to solve are for the cost of the phones and the number of phones: 35x + 50y = 2220 x + y = 51 One way to solve a linear system of equations is to multiply every term in one of them by a single constant, so that the coefficient of one variable in each equation is the same, then subtract the two equations from each other, solve for the remaining variable, then plug that into the original equations to get the first variable. I will multiply each term in the second equation by 35, then subtract it from the first: 35x + 50y = 2220 35x + 35y = (51)(35) = 1785 ==> 15y = 435 ==> y = 29 plugging into the second original equation: x + 29 = 51 ==> x = 22 To check, plug both into the first equation: 35(22) + 50(29) = 770 + 1450 = 2220 Therefore 22 model A4 and 29 model Z20 were sold.

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.