$MathMaster logo$

MathMaster

Home
general
a candy distributor needs to mix a 40 fat content chocolate with a 60 fat content chocolate to create 100 kilograms of a 4

Question

A candy distributor needs to mix a 40% fat-content chocolate with a 60% fat-content chocolate to create 100 kilograms of a 40% fat-content chocolate. How many kilograms of each kind of chocolate must they use?

199

likes

997 views

Answer to a math question A candy distributor needs to mix a 40% fat-content chocolate with a 60% fat-content chocolate to create 100 kilograms of a 40% fat-content chocolate. How many kilograms of each kind of chocolate must they use?

$Expert avatar$

4.5

107 Answers

Let's assume that the distributor needs to use x kilograms of the 40% fat-content chocolate and y kilograms of the 60% fat-content chocolate.

We know that the total weight of the mixture is 100 kilograms, so x + y = 100.

Since the desired fat content of the mixture is 40%, we can set up the equation for the fat content as:

(0.40)(x) + (0.60)(y) = (0.40)(100).

Now we can solve these two equations simultaneously to find the values of x and y.

From the first equation, we can solve for y:

y = 100 - x.

Substituting this into the second equation, we have:

(0.40)(x) + (0.60)(100 - x) = (0.40)(100).

Simplifying the equation, we get:

0.40x + 60 - 0.60x = 40.

Combining like terms, we have:

-0.20x + 60 = 40.

Subtracting 60 from both sides, we get:

-0.20x = -20.

Dividing both sides by -0.20, we get:

x = 100.

Substituting this value of x back into the first equation, we have:

y = 100 - x = 100 - 100 = 0.

Therefore, the distributor needs to use 100 kilograms of the 40% fat-content chocolate and 0 kilograms of the 60% fat-content chocolate to create a 100-kilogram mixture with a 40% fat content.

Answer: The distributor needs to use 100 kilograms of the 40% fat-content chocolate and 0 kilograms of the 60% fat-content chocolate.

Frequently asked questions (FAQs)

What is the slope of a line passing through (2, 4) and (-3, 5)?

+

What is the basis of vectors in a given space with dimension 3?

+

Find the real root(s) of the cubic equation x^3 - 6x^2 + 11x - 6 = 0.

+

New questions in Mathematics

The sum of an infinite geometric series is 13,5 The sum of the same series, calculated from the third term is 1,5. Q. Calculate r if r>0.

Find the equation of the normal to the curve y=x²+4x-3 at point(1,2)

Write 32/25 as a percent

An integer is taken at random from the first 40 positive integers. What is the probability that the integer is divisible by 5 or 6?

Margin of error E=0.30 populations standard deviation =2.5. Population means with 95% confidence. What I the required sample size (round up to the whole number)

What’s the slope of a tangent line at x=1 for f(x)=x2. We can find the slopes of a sequence of secant lines that get closer and closer to the tangent line. What we are working towards is the process of finding a “limit” which is a foundational topic of calculus.

The physician orders 15mg of tramadol(liquid). On hand is 30mg/2mL vials. How many mL will the MA administer?

A box of numbered pens has 12 red, 12 blue, 12 green and 12 yellow pens. The pens for each colour are numbered from 1 to 12. There is a unique number on each pen, so no pen is exactly the same as any other pen in the box. When reaching into the box to randomly draw five pens without replacement, what is the proportion of getting exactly four pens of the same colour (Note: the numbers matter but the order does not)?

If a two-branch parallel current divider network, if the resistance of one branch is doubled while keeping all other factors constant, what happens to the current flow through that branch and the other branch? Select one: a. The current through the doubled resistance branch remains unchanged, and the current through the other branch decreases. b. The current through the doubled resistance branch decreases, and the current through the other branch remains unchanged. c. The current through the doubled resistance branch increases, and the current through the other branch remains unchanged. d. The current through both branches remain unchanged.

From 1975 through 2020 the mean annual gain of the Dow Jones Industrial Average was 652. A random sample of 34 years is selected from this population. What is the probability that the mean gain for the sample was between 400 and 800? Assume the standard deviation is 1539

TEST 123123+1236ttttt

9.25=2pi r solve for r

Find the minimum value of the function y = -4 x3 + 60 x2 -252 x + 8 for values of x between x = 0 and x = 9 Enter the value of the function, not the value of x

In poker, a full house consists of five cards, where two of the cards have the same number (or letter) and the remaining three also have the same number (or letter) as each other (but not as the previous two cards). Use a search engine or Wikipedia to understand the concept better if necessary. In how many different ways can one obtain a full house?

A psychologist is investigating the levels of test anxiety in various university courses. Anxiety is measured on a scale ranging from 0 to 100, where 0 indicates the complete absence of anxiety and 100 represents an extreme level of anxiety. From the data obtained, it has been discovered that the psychology score is triple that of nursing, and in turn, the latter has a score 10 points lower than the nutrition major. Furthermore, the score in the veterinary degree is 15 points higher than that of nutrition. Finally, if we add the scores of all the races, we will obtain a total of 173 points. Pose the equation that represents the situation described in the previous problem and determine: What is the score that psychology obtained regarding its anxiety level before the exams?

The area bounded by the curve y=ln(x) and the lines x=1 and x=4 above the x−axis is

Given two lines 𝐿1: 𝑥 + 4𝑦 = −10 and 𝐿2: 2𝑥 − 𝑦 = 7. i. Find the intersection point of 𝐿1 and 𝐿2.

Emile organizes a community dance to raise funds. In addition to paying $300 to rent the room, she must rent chairs at $2 each. The quantity of chairs rented will be equal to the number of tickets sold. She sells tickets for $7 each. How much should she sell to raise money?