A candy maker has 300mL300\operatorname{\mathrm{m}\mathrm{L}} of a 45%45\% sugar syrup. She wants to dilute it with pure water to make a 30%30\% syrup. How many mLmL of water should she add?

150 mL ⁡ 150\operatorname{\mathrm{m}\mathrm{L}}

A candy maker has 300 mL 300\operatorname{\mathrm{m}\mathrm{L}} of a 45 % 45\% sugar syrup. She wants to dilute it with pure water to make a 30 % 30\% syrup. How many m L mL of water should she add?

In this problem, a candy maker has 300 milliliters of a 45% sugar syrup. She wants to dilute it with pure water to make it a 30% syrup. So how many milliliters of water should be added? To solve this problem, let's draw a picture. Let's say that this rectangle here represents the total amount of syrup at the end. And we know that we want this syrup to be 30% sugar. We don't know how much syrup there's going to be. So let's go ahead and name that a variable x milliliters. Now, to create this 30% syrup, we're gonna have two parts. One part of this is going to be our 300 milliliters of 45% sugar syrup. And the other part is going to be pure water. So what percent of water is sugar? Well, 0%. So the other part will be 0% sugar, and we don't know how much of that there's going to be, so let's go ahead and name that a variable as well, and we'll call that y milliliters. So now we're ready to build our equation. We know that to create our total with our percents we need to take our 30% syrup as a decimal is 0.3, multiply it by the amount of syrup which is x, and that is going to be equal to our 45% as a decimal is 0.45, times that amount, which is 300 milliliters, and we're gonna add to it our 0%, which is zero times that amount which is y. Now zero times y is just zero. So this simplifies to just 0.3 x is equal to 0.45 times 300. And since we only have one variable here, we can go ahead and solve for x. So simplifying, we get 0.3 x is equal to 0.45 times 300 is 135, and then divide both sides by 0.3, and we get that x is equal to four fifty. Now remember x represents the total amount of sugar syrup, which we get when we combine our part that is 45% sugar with our pure water. And what we want to know in this problem is how many milliliters of water should have been added. So what's another equation that we could write that relates our quantities x and Y? Well, to get our total amount of syrup, four fifty milliliters, we would add our 300 milliliters of 45% with our Y amount of water. And solving for y, we subtract 300 from both sides, and we get that y is equal to 150. So, that means the amount of water that we need to add is 150 milliliters.

A candy maker has 300 mL ⁡ 300\operatorname{\mathrm{m}\mathrm{L}} of a 45 % 45\% sugar syrup. She wants to dilute it with pure water to make a 30 % 30\% syrup. How many m L mL of water should she add?

150 mL ⁡ 150\operatorname{\mathrm{m}\mathrm{L}}

450 mL ⁡ 450\operatorname{\mathrm{m}\mathrm{L}}

750 mL ⁡ 750\operatorname{\mathrm{m}\mathrm{L}}

250 mL ⁡ 250\operatorname{\mathrm{m}\mathrm{L}}

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Beginning & Intermediate Algebra

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Mixture Problem Solving

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Multiple Choice

A candy maker has $300 mL$ of a $45 percent sign$ sugar syrup. She wants to dilute it with pure water to make a $30 percent sign$ syrup. How many $m L$ of water should she add?

$450 mL$

$750 mL$

$150 mL$

$250 mL$

Verified step by step guidance

Identify the amount of sugar in the original syrup by multiplying the volume of the syrup by its sugar concentration: calculate $300 \operatorname{mL} \times 0.45$ to find the sugar content in milliliters.

Let $x$ represent the amount of pure water (0% sugar) to be added. The total volume after adding water will be \$300 + x$ milliliters.

Set up an equation for the final concentration of sugar after dilution. The amount of sugar remains the same, but the total volume changes, so the concentration is $\frac{\text{sugar amount}}{300 + x} = 0.30$.

Substitute the sugar amount from step 1 into the equation: $\frac{300 \times 0.45}{300 + x} = 0.30$.

Solve the equation for $x$ by multiplying both sides by $(300 + x)$, then isolating $x$ on one side to find the volume of water to add.

5:18m

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A candy maker has 300mL300\(\operatorname{\mathrm{m}\]\mathrm{L}\)} of a 45%45\% sugar syrup. She wants to dilute it with pure water to make a 30%30\% syrup. How many mLmL of water should she add?

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A candy maker has $300 mL$ of a $45 percent sign$ sugar syrup. She wants to dilute it with pure water to make a $30 percent sign$ syrup. How many $m L$ of water should she add?