The community center has $100 to purchase new basketballs that cost $16.55 each and soccer balls that cost $14.75 each, where x is the number of purchased basketballs and y is the number of purchased soccer balls. which inequality represents this situation? enter your answer, in standard form, in the box.

16.55x +14.75y ≤ 100

Step-by-step explanation:

The sum of costs must not exceed the budget amount. The sum of costs is the sum of products of cost and quantity.

The problem statement tells us x is the number of basketballs and $16.55 is their price. This means 16.55x will be the total price of purchased basketballs.

Likewise, y is the number of soccer balls, and $14.75 is their price. 14.75y will be the total price of the purchased soccer balls.

The total of both purchases is then ...

... 16.55x + 14.75y

and this value must be less than or equal to $100. The inequality is written ...

... 16.55x +14.75y ≤ 100

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step-by-step explanation:

starting with:    

5 + x - 12 = 2x - 7   

5 + x - 12 - x = 2x - 7 - x (subtract x from both sides)   

5 - 12 = x - 7 (combine and cancel x's from both sides)   

5 - 12 + 7 = x - 7 + 7 (add 7 to both sides)   

0 = x (add numbers together on both sides)       

so in order for the equation to be true, x must be 0.   

trying x = -0.5   

5 + x - 12 = 2x - 7 (original equation)   

5 + -0.5 - 12 = 2(-0.5) - 7 (plug in value of x)   

5 + -0.5 - 12 = -1 - 7 (did multiplication)   

-7.5 = -8 (did addition on both sides)       

since -7.5 is obviously not equal to -8, the value of -0.5 for x is wrong.   

trying x = 0   

5 + x - 12 = 2x - 7 (original equation)   

5 + 0 - 12 = 2(0) - 7 (plug in value of x)   

5 + 0 - 12 = 0 - 7 (did multiplication)   

-7 = -7 (did addition on both sides)       

since -7 equals -7, that demonstrates that the value of 0 for x is correct.   

trying x = 1   

5 + x - 12 = 2x - 7 (original equation)   

5 + 1 - 12 = 2(1) - 7 (plug in value of x)   

5 + 1 - 12 = 2 - 7 (did multiplication)   

-6 = -5 (did addition on both sides)       

since -6 is obviously not equal to -5, the value of 1 for x is wrong.