Question

susie is visiting the u.s. from mexico. one day she stopped by a market and found a stall selling tomatoes for 0.83 dollars per pound. if 1 peso was worth 0.053 dollars that day, how much did the tomatoes cost in pesos per kilogram?
first fill in the two blanks on the left side of the equation using two of the ratios. then write your answer rounded to the nearest hundredth on the right side of the equation.
ratios:
\\(\frac{1\text{ kg}}{2.2\text{ lb}}\\)
\\(\frac{2.2\text{ lb}}{1\text{ kg}}\\)
\\(\frac{1\text{ peso}}{0.053\text{ dollars}}\\)
\\(\frac{0.053\text{ dollars}}{1\text{ peso}}\\)
\\(\frac{0.83\text{ dollars}}{1\text{ lb}}\\) × \\(\square\\) × \\(\square\\) = \\(\frac{\text{pesos}}{\text{kg}}\\)

Explanation:

Step1: Convert pounds to kilograms

We know the ratio for converting kilograms to pounds is $\frac{1\ \text{kg}}{2.2\ \text{lb}}$, but we need to convert pounds to kilograms. So the ratio should be $\frac{2.2\ \text{lb}}{1\ \text{kg}}$ inverted? Wait, no. Wait, we have price per pound ($0.83$ dollars per $1$ lb) and we need to find per kg, then convert dollars to pesos. Wait, first, let's set up the unit conversion.

We have: $\frac{0.83\ \text{dollars}}{1\ \text{lb}} \times \frac{2.2\ \text{lb}}{1\ \text{kg}}$ (this converts pounds to kilograms, so lb cancels, giving dollars per kg)

Step2: Convert dollars to pesos

Now, we need to convert dollars to pesos. The exchange rate is $0.053$ dollars per $1$ peso, so to convert dollars to pesos, we use the ratio $\frac{1\ \text{peso}}{0.053\ \text{dollars}}$ (because we want dollars to cancel and pesos to be in the numerator).

So the second ratio is $\frac{1\ \text{peso}}{0.053\ \text{dollars}}$

Now, multiply the three terms:

First, $\frac{0.83\ \text{dollars}}{1\ \text{lb}} \times \frac{2.2\ \text{lb}}{1\ \text{kg}} \times \frac{1\ \text{peso}}{0.053\ \text{dollars}}$

Now, let's calculate the numerical value:

First, multiply $0.83 \times 2.2 = 1.826$

Then, divide by $0.053$: $\frac{1.826}{0.053} \approx 34.45$ (rounded to the nearest hundredth)

Wait, let's do it step by step:

$0.83 \times 2.2 = 1.826$ (dollars per kg)

Then, $1.826 \div 0.053 \approx 34.45$ (pesos per kg)

Wait, let's check the unit conversions:

- $\frac{0.83\ \text{dollars}}{1\ \text{lb}} \times \frac{2.2\ \text{lb}}{1\ \text{kg}}$: lb cancels, so we have $\frac{0.83 \times 2.2\ \text{dollars}}{1\ \text{kg}} = \frac{1.826\ \text{dollars}}{1\ \text{kg}}$

- Then, $\frac{1.826\ \text{dollars}}{1\ \text{kg}} \times \frac{1\ \text{peso}}{0.053\ \text{dollars}}$: dollars cancel, so we have $\frac{1.826}{0.053}\ \text{pesos per kg} \approx 34.45\ \text{pesos per kg}$

So the blanks are: first blank $\frac{2.2\ \text{lb}}{1\ \text{kg}}$, second blank $\frac{1\ \text{peso}}{0.053\ \text{dollars}}$, and the final answer is approximately $34.45$ pesos per kg.

Wait, let's re-express the steps with the given ratios. The ratios provided are:

- $\frac{1\ \text{kg}}{2.2\ \text{lb}}$

- $\frac{2.2\ \text{lb}}{1\ \text{kg}}$

- $\frac{1\ \text{peso}}{0.053\ \text{dollars}}$

- $\frac{0.053\ \text{dollars}}{1\ \text{peso}}$

We need to convert from dollars per lb to pesos per kg. So:

1. Convert lb to kg: we have dollars per lb, so to get dollars per kg, we multiply by lb per kg (since 1 kg = 2.2 lb, so lb per kg is 2.2 lb / 1 kg). So the first ratio is $\frac{2.2\ \text{lb}}{1\ \text{kg}}$? Wait, no: if we have $\frac{0.83\ \text{dollars}}{1\ \text{lb}}$, and we want to multiply by a ratio that cancels lb and gives kg in the denominator. So the ratio should be $\frac{2.2\ \text{lb}}{1\ \text{kg}}$? Wait, no, 1 kg = 2.2 lb, so $\frac{2.2\ \text{lb}}{1\ \text{kg}} = 1$ (since 2.2 lb = 1 kg). So multiplying $\frac{0.83\ \text{dollars}}{1\ \text{lb}} \times \frac{2.2\ \text{lb}}{1\ \text{kg}}$ gives $\frac{0.83 \times 2.2\ \text{dollars}}{1\ \text{kg}}$, which is dollars per kg.

Then, to convert dollars to pesos, we use the ratio $\frac{1\ \text{peso}}{0.053\ \text{dollars}}$ (because 0.053 dollars = 1 peso, so 1 peso / 0.053 dollars is the conversion factor to get pesos from dollars).

So the two blanks are:

First blank: $\frac{2.2\ \text{lb}}{1\ \text{kg}}$ (wait, no, wait: the first ratio given is $\frac{1\ \text{kg}}{2.2\ \text{lb}}$ and $\frac{2.2\ \text{lb}}{1\ \text{kg}}$. Wait, maybe I had it reversed. Let's think again.

Wait, we have:

We need to go from lb to kg. So if 1 kg = 2.2 lb, then 1 lb = 1/2.2 kg. So to convert lb to kg, we multiply by 1/2.2 kg per lb. But the ratio given is $\frac{1\ \text{kg}}{2.2\ \text{lb}}$, which is 1 kg per 2.2 lb. So if we have $\frac{0.83\ \text{dollars}}{1\ \text{lb}}$, and we multiply by $\frac{1\ \text{kg}}{2.2\ \text{lb}}$, that would give $\frac{0.83\ \text{dollars} \times 1\ \text{kg}}{1\ \text{lb} \times 2.2\ \text{lb}}$? No, that's wrong. Wait, no, units: lb in numerator and denominator. Wait, no, $\frac{0.83\ \text{dollars}}{1\ \text{lb}} \times \frac{1\ \text{kg}}{2.2\ \text{lb}}$ would have lb in the denominator twice, which is wrong. Oh! I made a mistake earlier.

Correct unit conversion: To convert from dollars per lb to dollars per kg, we need to multiply by the number of pounds in a kilogram, because 1 kg = 2.2 lb. So dollars per kg = dollars per lb × pounds per kg. So pounds per kg is 2.2 lb / 1 kg. So the ratio is $\frac{2.2\ \text{lb}}{1\ \text{kg}}$. Wait, no: if 1 kg = 2.2 lb, then 2.2 lb = 1 kg, so $\frac{2.2\ \text{lb}}{1\ \text{kg}} = 1$. So when we multiply $\frac{0.83\ \text{dollars}}{1\ \text{lb}} \times \frac{2.2\ \text{lb}}{1\ \text{kg}}$, the lb cancels, giving $\frac{0.83 \times 2.2\ \text{dollars}}{1\ \text{kg}}$, which is correct (dollars per kg).

Then, to convert dollars to pesos: we know that 0.053 dollars = 1 peso, so 1 dollar = 1 / 0.053 pesos. So the ratio to convert dollars to pesos is $\frac{1\ \text{peso}}{0.053\ \text{dollars}}$ (because dollars in numerator and denominator cancel, leaving pesos).

So now, multiplying the three terms:

$\frac{0.83\ \text{dollars}}{1\ \text{lb}} \times \frac{2.2\ \text{lb}}{1\ \text{kg}} \times \frac{1\ \text{peso}}{0.053\ \text{dollars}}$

Now, let's check units:

- dollars (numerator) × lb (numerator) × peso (numerator)

- lb (denominator) × kg (denominator) × dollars (denominator)

So lb cancels (numerator and denominator), dollars cancels (numerator and denominator), leaving peso / kg, which is what we want.

Now, calculate the numerical value:

First, multiply 0.83 and 2.2: $0.83 \times 2.2 = 1.826$

Then, divide by 0.053: $1.826 \div 0.053 \approx 34.45$ (rounded to the nearest hundredth)

So the first blank is $\frac{2.2\ \text{lb}}{1\ \text{kg}}$, the second blank is $\frac{1\ \text{peso}}{0.053\ \text{dollars}}$, and the final answer is approximately $34.45$ pesos per kg.

Answer:

The two blanks are $\frac{2.2\ \text{lb}}{1\ \text{kg}}$ and $\frac{1\ \text{peso}}{0.053\ \text{dollars}}$, and the cost of tomatoes is approximately $\boxed{34.45}$ pesos per kg.