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Helen [10]
3 years ago
6

A pet store sells goldfish and hermit crabs,

Mathematics
1 answer:
Elis [28]3 years ago
5 0

Answer:

Cost = \$28

Step-by-step explanation:

Given

Represent Goldfish with g and hermit crabs with h.

The first statement, we have:

7g + 3h = 26

The second statement, we have:

4g + 5h = 28

Required

Determine the selling price of 6 goldfish and 4 hermit crabs

The equations are:

7g + 3h = 26 --- (1)

4g + 5h = 28 --- (2)

Make g the subject in (2)

4g + 5h = 28

4g = 28 - 5h

Divide both sides by 4

g = \frac{1}{4}(28 - 5h)

Substitute \frac{1}{4}(28 - 5h) for g in (1)

7g + 3h = 26

7(\frac{1}{4}(28 - 5h)) + 3h = 26

\frac{7}{4}(28 - 5h) + 3h = 26

Multiply through by 4

4 * \frac{7}{4}(28 - 5h) + 4*3h = 26*4

7(28 - 5h) + 4*3h = 26*4

Open bracket

196 - 35h + 12h = 104

196 -23h = 104

Collect Like Terms

-23h = 104-196

-23h = -92

Make h the subject

h = \frac{-92}{-23}

h = \frac{92}{23}

h = 4

Substitute 4 for h in g = \frac{1}{4}(28 - 5h)

g = \frac{1}{4}(28 - 5*4)

g = \frac{1}{4}(28 - 20)

g = \frac{1}{4}(8)

g = 2

This implies that:

1 goldfish = $2

1 hermit crab = $4

The cost of 6 goldfish and 4 hermit crabs is:

Cost = 6g + 4h

Cost = 6*\$2 + 4*\$4

Cost = \$12 + \$16

Cost = \$28

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At the local gas station gasoline costs $2.75 for per gallon and diesel costs $3.02 per gallon. Gabriel needs to purchase 15.2 g
Ainat [17]

Answer:

The total amount paid by Gabriel at the local gas station is $70.49.

Step-by-step explanation:

Cost of gasoline per gallon = $2.75

Cost of diesel per gallon = $3.02

Amount of gasoline Gabriel needs = 15.2 gallons

Amount of diesel Gabriel needs = 9.5 gallons

Compute the total amount paid by Gabriel at the local gas station as follows:

Total Cost = Cost of gasoline × Amount of gasoline

                           + Cost of diesel × Amount of diesel

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Thus, the total amount paid by Gabriel at the local gas station is $70.49.

7 0
3 years ago
What is the greatest common factor of 44c^5, 22c^3 and 11c^4
Alexxandr [17]

\text{ GCF of } 44c^5, 22c^3 , 11c^4 \text{ is } 11c^3

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

Given that, we have to find the greatest common factor of 44c^5, 22c^3 , 11c^4

The greatest number that is a factor of two (or more) other numbers.

When we find all the factors of two or more numbers, and some factors are the same ("common"), then the largest of those common factors is the Greatest Common Factor

\underline{\text{ GCF of } 44c^5, 22c^3 , 11c^4 :}

First find the GCF of numbers and then find the GCF of variables and then multiply them together

<em><u>Step 1: GCF of 44, 22 and 11</u></em>

The factors of 11 are: 1, 11

The factors of 22 are: 1, 2, 11, 22

The factors of 44 are: 1, 2, 4, 11, 22, 44

11 is the greatest factor that is common in above three list

Then the greatest common factor is 11

\text{ Step 2: GCF of }c^5, c^3 , c^4

c^5 = c^3 \times c^2\\\\c^3 = c^2 \times c^1 \text{ or } c^3\\\\c^4 = c^3 \times c^1

Thus the greatest common factor is c^3

Step 3: Multiply the GCF of 44, 22, 11 and GCF of c^5, c^3 , c^4

\text{ GCF of } 44c^5, 22c^3 , 11c^4 = 11 \times c^3 = 11c^3

Thus \text{ GCF of } 44c^5, 22c^3 , 11c^4 \text{ is } 11c^3

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Step-by-step explanation:

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