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2 years ago

9

How much cashews at $1.58 per pound must be mixed with walnuts that cost 78 cents per pound to make a mixture of 40 pounds of nu

ts that cost $1.50 per pound?

2 answers:

Likurg_2 [28]2 years ago

5 0

Number of pounds of cashews is 36 pounds and number of pounds of walnuts is 4 pounds.

Step-by-step explanation:

Step 1: Given details are cost of cashews = $1.58, cost of walnuts = 78 cents = $0.78, total weight of nuts = 40 pounds, cost of nuts per pound = $1.50

Step 2: Let number of pounds of cashews to be mixed be C, then number of pounds of walnuts will 40 - C. Form equation with these variables.

⇒ 1.58 C + (40-C) 0.78 = 40 × 1.50

⇒ 1.58 C + 31.2 - 0.78 C = 60

⇒ 1.58 C - 0.78 C = 60 - 31.2

⇒ 0.8 C = 28.8

⇒ C = 36 pounds

Step 3: Calculate number of pounds of walnuts

⇒ Number of pounds of walnuts = 40 - C = 4 pounds

pogonyaev2 years ago

5 0

Answer:

36 pounds cashews

4 pounds walnuts

Step-by-step explanation:

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The sum of two numbers is 36 . The larger number is 22 more than the smaller number. What are the numbers?

Setler [38]

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x = y + 22

y + 22 + y = 36
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y = 14/2
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It takes 54 minutes for 4 people to paint 6 walls. How many minuets does it take 6 people to paint 7 walls?

earnstyle [38]

It takes 42 minutes for 6 people to paint 7 walls

<em><u>Solution:</u></em>

It takes 54 minutes for 4 people to paint 6 walls

To find: Minutes required for 6 people to paint 7 walls

If $M_1$ men can do $W_1$ work in $D_1$ days working $H_1$ hours per day and $M_2$ men can do $W_2$ work in $D_2$ days working $H_2$ hours per day, then

$\frac{M_1D_1H_1}{W_1} = \frac{M_2D_2H_2}{W_2}$

M = Number of men

D = Number of days

H = Number of hours per day

W = Amount of work

Here in this sum,

<em><u>54 minutes for 4 people to paint 6 walls</u></em>

$H_1 = 54 minutes ; M_1 = 4 people ; W_1 = 6 walls$

<em><u>Minutes required for 6 people to paint 7 walls</u></em>

$H_2 = ? ; M_2 = 6 people ; W_2 = 7 walls$

<em><u>Substituting the values in formula, we get</u></em>

$\frac{54 \times 4}{6} = \frac{H_2 \times 6}{7}\\\\9 \times 4 = \frac{H_2 \times 6}{7}\\\\H_2 = \frac{36 \times 7}{6}\\\\H_2 = 42$

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The current population of a town is 10,000 and its growth in years can be represented by P(t) = 10,000(0.2)^t, where t is the ti

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Answer:

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Step-by-step explanation:

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1) $P(0)$ is the population initially.

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$\frac{P(1)}{P(0)}$ represents the population increase factor.

So let's evaluate that fraction:

$\frac{P(1)}{P(0)}$

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$\frac{0.2^1}{0.2^0}=\frac{0.2}{1}=0.2$

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2) Let's figure out the population growth in terms of months instead of years.

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We want t to represent months.

A full year is 12 months, in a full year we have that $P(1)=10000(0.2)^1=10000(0.2)=2000$

So we want a new P such that $P(12)=2000$ since 12 months equals a year.

Let's look at the functions given to see which gives us this:

a) $P(12)=10000(0.87449)^{12}=2000 \text{approximately}$

b) $P(12)=10000(0.87449)^{12(12)}=0 \text{ approximately}$

c) $P(12)=10000(0.87449)^{\frac{1}{12}}=9889 \text{approximately}$

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So a is the function we want.

Also another way to look at this:

$P(t)=10000(.2)^t$ where $t$ is in years.

$P(t)=10000(.2^\frac{1}{12})^t$ where $t$ is in months.

And $.2^\frac{1}{12}=0.874485 \text{approximately}$

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vekshin1

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