Question

at xochitl’s store, the cost of nine bars of soap is $33.09. at christian’s store, the cost of ten bars of the same soap is $37.37. compare prices by finding a pair of common values (same number of soap bars or same price). round your answers to the nearest cent if necessary.
answer attempt 1 out of 2
at xochitl’s store, \boxed{} bars of soap cost $\boxed{}. at christian’s store, \boxed{} bars of soap cost $\boxed{}. \space store has the better price.

Explanation:

Step1: Find unit price for Xochitl's store

To find the unit price (price per bar) at Xochitl's store, we divide the total cost by the number of bars. So, the unit price \( p_{X} = \frac{33.09}{9} \). Calculating this, \( 33.09 \div 9 = 3.676\ldots \approx 3.68 \) dollars per bar.

Step2: Find unit price for Christian's store

For Christian's store, the unit price \( p_{C} = \frac{37.37}{10} = 3.737 \approx 3.74 \) dollars per bar.

Step3: Compare prices for 90 bars (LCM of 9 and 10)

To find a common number of bars, we can use the least common multiple of 9 and 10, which is 90.
- For Xochitl's store, cost for 90 bars: \( 90 \times 3.68 = 331.20 \) dollars.
- For Christian's store, cost for 90 bars: \( 90 \times 3.74 = 336.60 \) dollars. (Alternatively, since Christian's has 10 bars for 37.37, for 90 bars it's \( 9 \times 37.37 = 336.33 \) dollars (more accurate as we use the original total cost for 10 bars). Wait, maybe better to use the original total cost scaling. Let's recalculate:
Wait, actually, to find cost for 90 bars at Xochitl's: since 9 bars cost 33.09, 90 bars is 10 times that, so \( 33.09 \times 10 = 330.90 \) dollars.
At Christian's, 10 bars cost 37.37, so 90 bars is 9 times that, \( 37.37 \times 9 = 336.33 \) dollars.

Step4: Compare costs

Now, we can see that for 90 bars, Xochitl's store costs $330.90 and Christian's costs $336.33. So Xochitl's is cheaper.
Alternatively, using unit prices: Xochitl's unit price is ~$3.68, Christian's is ~$3.74. So per bar, Xochitl's is cheaper.

Let's fill the blanks with a common number of bars, say 90 (or we can use 10 and 9, but let's use 90 for clarity).
- At Xochitl's store, 90 bars of soap cost \( 90 \times 3.676\ldots = 330.90 \) (since 9 bars cost 33.09, 90 is 10*9, so 10*33.09 = 330.90).
- At Christian's store, 90 bars of soap cost \( 9 \times 37.37 = 336.33 \) (since 10 bars cost 37.37, 90 is 9*10, so 9*37.37 = 336.33).

Or, using 10 bars for Xochitl's: wait, no, Xochitl's has 9 bars. Alternatively, use 1 bar: but the problem says "a pair of common values (same number of soap bars or same price)". So we can use the same number of bars (like 90) or same price. Let's use same number of bars (90) as a common value.

So:
At Xochitl's store, 90 bars of soap cost $330.90. At Christian's store, 90 bars of soap cost $336.33. Xochitl's store has the better price.

Alternatively, using 1 bar:
At Xochitl's store, 1 bar of soap cost $3.68. At Christian's store, 1 bar of soap cost $3.74. Xochitl's store has the better price.

Let's check the unit prices again:
Xochitl: 33.09 / 9 = 3.676666... ≈ 3.68 (rounded to nearest cent)
Christian: 37.37 / 10 = 3.737 ≈ 3.74 (rounded to nearest cent)

So if we use 1 bar as the common number of bars:
At Xochitl's store, 1 bar of soap cost $3.68. At Christian's store, 1 bar of soap cost $3.74. Xochitl's store has the better price.

Or, use 9 bars for Christian's? Wait, Christian's has 10 bars. Maybe the problem expects using the same number of bars by scaling. Let's go with unit price (1 bar) as the common "number of bars" (1 bar) or same price.

So filling the blanks:

At Xochitl's store, 1 bars of soap cost $3.68. At Christian's store, 1 bars of soap cost $3.74. Xochitl's store has the better price.

Or, using 90 bars:

At Xochitl's store, 90 bars of soap cost $330.90. At Christian's store, 90 bars of soap cost $336.33. Xochitl's store has the better price.

Let's verify the unit price calculation again:

Xochitl: 33.09 ÷ 9 = 3.676666..., which is $3.68 when rounded to the nearest cent.

Christian: 37.37 ÷ 10 = 3.737, which is $3.74 when rounded to the nearest cent.

So comparing the unit prices, Xochitl's is cheaper.

Answer:

At Xochitl's store, \(\boldsymbol{1}\) bars of soap cost \(\boldsymbol{\$3.68}\). At Christian's store, \(\boldsymbol{1}\) bars of soap cost \(\boldsymbol{\$3.74}\). \(\boldsymbol{Xochitl's}\) store has the better price.

(Alternatively, using 90 bars: At Xochitl's store, \(\boldsymbol{90}\) bars of soap cost \(\boldsymbol{\$330.90}\). At Christian's store, \(\boldsymbol{90}\) bars of soap cost \(\boldsymbol{\$336.33}\). \(\boldsymbol{Xochitl's}\) store has the better price. Either way, the key is that Xochitl's is cheaper.)