A sports store sells basketballs and soccer balls. Basketballs cost $15, and soccer balls cost $20. If the store sells 25 items and earns $400, what system of equations represents the situation?
a. $20 x+15 y=25, x+y=400$
b. $15 x+20 y=25, x+y=400$
c. $20 x+15 y=400, x+y=25$
d. $15 x+20 y=400, x+y=25

Question

A sports store sells basketballs and soccer balls. Basketballs cost $15, and soccer balls cost $20. If the store sells 25 items and earns $400, what system of equations represents the situation? 
a. $20 x+15 y=25, x+y=400$ 
b. $15 x+20 y=25, x+y=400$ 
c. $20 x+15 y=400, x+y=25$ 
d. $15 x+20 y=400, x+y=25

GinnyAnswer · Answer

Define variables: Let x be the number of basketballs and y be the number of soccer balls. 
 Write the equation for the total number of items: x + y = 25 . 
 Write the equation for the total earnings: 15 x + 20 y = 400 . 
 The system of equations is: x + y = 25 and 15 x + 20 y = 400 , so the answer is d ​ . 
 
 Explanation 
 
 Problem Analysis Let's analyze the problem. We are given that a sports store sells basketballs and soccer balls. We know the price of each basketball is $15 and each soccer ball is $20. The store sells a total of 25 items and earns $400. We need to determine the system of equations that represents this situation. 
 
 Define Variables Let's define our variables: Let x be the number of basketballs sold. Let y be the number of soccer balls sold. 
 
 Equation for Total Items We know that the total number of items sold is 25. This gives us our first equation: x + y = 25 
 
 Equation for Total Earnings We also know that the total earnings is $400. The earnings from basketballs is 15 x , and the earnings from soccer balls is 20 y . This gives us our second equation: 15 x + 20 y = 400 
 
 System of Equations Therefore, the system of equations that represents this situation is: x + y = 25 15 x + 20 y = 400 This corresponds to option d.

Examples 
 Imagine you're organizing a school sports event and need to order equipment. Knowing the prices of basketballs and soccer balls, and the total budget, you can use a system of equations to determine how many of each ball you can afford. This helps in planning and managing resources effectively, ensuring you stay within budget while getting the necessary equipment for the event. Similarly, small business owners can use such systems to manage inventory and sales.

Answer (1)

Related Questions in Mathematics

📝 Answered - Select the correct answer. Which equation is equivalent to the given equation? [tex]$x^2-6 x=8$[/tex] A. [tex]$(x-6)^2=44$[/tex] B. [tex]$(x-3)^2=17$[/tex] C. [tex]$(x-6)^2=20$[/tex] D. [tex]$(x-3)^2=14$[/tex]

📝 Answered - Which phrase best describes the translation from the graph [tex]y=6 x^2[/tex] to the graph of [tex]y=6(x+1)^2[/tex]? A. 6 units left B. 6 units right C. 1 unit left D. 1 unit right

📝 Answered - What expression is equivalent to [tex]$\left(5 z^2+3 z+2\right)^2$[/tex] ? A. [tex]$5 z^4+3 z^2+4$[/tex] B. [tex]$5 z^4+9 z^2+4$[/tex] C. [tex]$25 z^4+30 z^3+19 z^2+12 z+4$[/tex] D. [tex]$25 z^4+30 z^3+29 z^2+12 z+4$[/tex]

📝 Answered - The graph of [tex]y=\frac{5}{4} x+1[/tex] is shown below. The coordinate ([tex]0, y[/tex]) is a solution of the equation. Given the [tex]x[/tex]-value of 0, what is the value of the [tex]y[/tex]-coordinate for the coordinate ([tex]0, y[/tex])? [tex]y=[/tex] [blank]

📝 Answered - If [tex]f(-2)=0[/tex], what are all the factors of the function [tex]f(x)=x^3-2 x^2-68 x-120[/tex]? Use the Remainder Theorem. A. [tex](x+2)(x+60)[/tex] B. [tex](x-2)(x-60)[/tex] C. [tex](x-10)(x+2)(x+6)[/tex] D. [tex](x+10)(x-2)(x-6)[/tex]