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It is recommended that
7.8mL of Grow-It-Right plant food be mixed with
2L of water for feeding houseplants. How much plant food should be mixed with
1gal of water to maintain the same concentration? (
1gal~~3.8L.) Express the answer in milliliters.

$21$ . It is recommended that $7.8 \mathrm{~mL}$ of Grow-It-Right plant food be mixed with $2 \mathrm{~L}$ of water for feeding houseplants. How much plant food should be mixed with $1 \mathrm{gal}$ of water to maintain the same concentration? ( $1 \mathrm{gal} \approx 3.8 \mathrm{~L}$ .) Express the answer in milliliters.

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Convert between customary and metric systems

Full solution

Q.

21

. It is recommended that

7.8 \mathrm{~mL}

of Grow-It-Right plant food be mixed with

2 \mathrm{~L}

of water for feeding houseplants. How much plant food should be mixed with

1 \mathrm{gal}

of water to maintain the same concentration? (

1 \mathrm{gal} \approx 3.8 \mathrm{~L}

.) Express the answer in milliliters.

Convert to Liters: First, convert gallons to liters because the recommendation is in milliliters per liter. We know $1$ gallon is approximately $3.8$ liters.
Calculate Plant Food Amount: Now, we need to find out how much plant food is needed for $3.8$ liters of water to keep the same concentration as $7.8$ mL for $2$ liters.
Set Up Proportion: Set up a proportion where $7.8\,\text{mL}$ is to $2\,\text{liters}$ as $x\,\text{mL}$ is to $3.8\,\text{liters}$ . So, $\frac{7.8}{2} = \frac{x}{3.8}$ .
Cross-Multiply: Cross-multiply to solve for $x$ : $7.8 \times 3.8 = 2 \times x$ .
Calculate Left Side: Calculate the left side: $7.8 \times 3.8 = 29.64$ .
Divide to Solve: Now, divide by $2$ to solve for $x$ : $29.64 / 2 = x$ .
Calculate Division: Calculate the division: $29.64 / 2 = 14.82$ .

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