Question

which is the better buy?
7-pack of jump ropes for $12.07
8-pack of jump ropes for $13.84
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Explanation:

Step1: Calculate unit price for 7 - pack

To find the unit price (price per jump rope) for the 7 - pack, we divide the total price by the number of jump ropes. The formula for unit price \( u\) is \( u=\frac{\text{Total Price}}{\text{Number of Items}}\). For the 7 - pack, total price is \(\$12.07\) and number of items is 7. So, \( u_1=\frac{12.07}{7}\approx1.7243\) dollars per jump rope.

Step2: Calculate unit price for 8 - pack

For the 8 - pack, total price is \(\$13.84\) and number of items is 8. Using the same unit price formula, \( u_2 = \frac{13.84}{8}=1.73\) dollars per jump rope. Wait, no, let's recalculate: \(13.84\div8 = 1.73\)? Wait, \(8\times1.73 = 13.84\)? Wait, \(8\times1.7 = 13.6\), \(8\times0.03=0.24\), so \(13.6 + 0.24 = 13.84\). And for the 7 - pack: \(12.07\div7\). Let's do the division: \(7\times1.72 = 12.04\), \(12.07-12.04 = 0.03\), so \(0.03\div7\approx0.0043\), so \(1.72 + 0.0043\approx1.7243\). So \(u_1\approx1.72\) (rounded to two decimal places) and \(u_2 = 1.73\)? Wait, no, I made a mistake. Wait \(13.84\div8\): \(8\times1.73 = 13.84\)? \(8\times1.7 = 13.6\), \(8\times0.03 = 0.24\), \(13.6+0.24 = 13.84\). So \(13.84\div8 = 1.73\). And \(12.07\div7\): \(7\times1.72 = 12.04\), remainder 0.03, so \(12.07\div7 = 1.7242857\approx1.72\) (when rounded to two decimal places). Wait, so the 7 - pack has a lower unit price? Wait, no, wait my calculation for 8 - pack: \(13.84\div8\). Let's do it again: \(8\times1.73 = 13.84\)? \(1.73\times8\): \(1\times8 = 8\), \(0.7\times8 = 5.6\), \(0.03\times8 = 0.24\); \(8 + 5.6=13.6+0.24 = 13.84\). So 8 - pack unit price is \(1.73\) dollars per jump rope. 7 - pack unit price is \(12.07\div7 = 1.7242857\approx1.72\) dollars per jump rope. So the 7 - pack has a lower unit price, so it's a better buy. Wait, maybe I miscalculated the 8 - pack. Wait \(13.84\div8\): \(8\times1.73 = 13.84\), yes. And \(12.07\div7 = 1.7242857\). So \(1.7242857<1.73\), so the 7 - pack is cheaper per unit. Wait, but the original problem's 8 - pack is highlighted? Maybe I made a mistake. Wait, let's check again. 7 - pack: \(\$12.07\) for 7. \(12.07\div7 = 1.7242857\) dollars per rope. 8 - pack: \(\$13.84\) for 8. \(13.84\div8 = 1.73\) dollars per rope. So the 7 - pack is cheaper, so it's a better buy.

Answer:

The 7 - pack of jump ropes for \(\$12.07\) is the better buy.