Answer: 12
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Explanation:
- j = number of jerseys ordered
- c = total cost in dollars
For company X, the equation is c = 10j + 115 where the 10j is the cost of buying all the jerseys (j of them). Then we tack on the flat fee of $115
The equation for company Y is c = 20j for similar reasoning as the previous company, but now each jersey costs $20. We don't add on anything else because there isn't an extra flat fee.
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We have this system
[tex]\begin{cases}c = 10j+115\\c = 20j\end{cases}[/tex]
which are the equations for company X and company Y in that order.
Both equations have 'c' on the left side. So we can equate the right hand sides and solve for j
20j = 10j+115
20j-10j = 115
10j = 115
j = 115/10
j = 11.50
Recall that j is the number of jerseys. It's not possible to order half a jersey, so we have to round to the nearest whole number. The question is: which way? We're right at the midpoint between j = 11 and j = 12. Let's check both values of j to see what the costs are for each company.
- j = 11 for company X leads to c = 10j+115 = 10*11+115 = 225
- j = 11 for company Y leads to c = 20j = 20*11 = 220
Company Y is the cheaper option if you bought 11 jerseys. But we want to know when company X is the better deal. Let's try j = 12
- j = 12 for company X leads to c = 10j+115 = 10*12+115 = 235
- j = 12 for company Y leads to c = 20j = 20*12 = 240
This time company X is the winner in terms of the best deal (aka cheapest cost). If j gets any bigger, then company X is still the winner. So we can see that the minimum order must be 12 jerseys if we want company X to be the cheapest option.
