Question

at yusuf’s store, the cost of nine tubes of tooth paste is $33.85. at owen’s store, the cost of six tubes of the same tooth paste is $22.99. compare prices by finding a pair of common values (same number of tooth paste tubes or same price). round your answers to the nearest cent if necessary.

answer attempt 1 out of 2

at yusuf’s store, □ tubes of tooth paste cost $ □. at owen’s store, □ tubes of tooth paste cost $ □. □ store has the better price.

Explanation:

Step1: Find LCM of 9 and 6

To find a common number of tubes, we find the least common multiple (LCM) of 9 and 6. Prime factors of 9: $3^2$, prime factors of 6: $2\times3$. So LCM is $2\times3^2 = 18$.

Step2: Calculate cost for 18 tubes at Yusuf's

Cost per tube at Yusuf's: $\frac{33.85}{9} \approx 3.7611$ dollars per tube. Cost for 18 tubes: $3.7611\times18 \approx 67.70$ dollars.

Step3: Calculate cost for 18 tubes at Owen's

Cost per tube at Owen's: $\frac{22.99}{6} \approx 3.8317$ dollars per tube. Cost for 18 tubes: $3.8317\times18 \approx 68.97$ dollars.

Alternatively, we can find the cost for 1 tube (unit price) or 18 tubes (as above). Let's check unit price:

Step1 (Alternative): Unit price at Yusuf's

Unit price (Yusuf's): $\frac{33.85}{9} \approx 3.76$ dollars (rounded to nearest cent).

Step2 (Alternative): Unit price at Owen's

Unit price (Owen's): $\frac{22.99}{6} \approx 3.83$ dollars (rounded to nearest cent).

Since we need a common number of tubes, let's use 18 (LCM of 9 and 6) or 1 tube (common price comparison). Let's use 18 tubes:

At Yusuf's store, 18 tubes of tooth paste cost $\approx 67.70$. At Owen's store, 18 tubes of tooth paste cost $\approx 68.97$. Yusuf's store has the better price.

Or using 1 tube:

At Yusuf's store, 1 tube of tooth paste cost $\approx 3.76$. At Owen's store, 1 tube of tooth paste cost $\approx 3.83$. Yusuf's store has the better price.

Let's use the LCM approach for common number of tubes (18):

Step1: LCM of 9 and 6 is 18.

Step2: Cost for 18 tubes at Yusuf's: $33.85\times\frac{18}{9} = 33.85\times2 = 67.70$

Step3: Cost for 18 tubes at Owen's: $22.99\times\frac{18}{6} = 22.99\times3 = 68.97$

Answer:

At Yusuf's store, 18 tubes of tooth paste cost $\$67.70$. At Owen's store, 18 tubes of tooth paste cost $\$68.97$. Yusuf's store has the better price.

(Alternatively, using 1 tube: At Yusuf's store, 1 tube of tooth paste cost $\$3.76$. At Owen's store, 1 tube of tooth paste cost $\$3.83$. Yusuf's store has the better price.)