Answer:
[tex]Cost = \$28[/tex]
Step-by-step explanation:
Given
Represent Goldfish with g and hermit crabs with h.
The first statement, we have:
[tex]7g + 3h = 26[/tex]
The second statement, we have:
[tex]4g + 5h = 28[/tex]
Required
Determine the selling price of 6 goldfish and 4 hermit crabs
The equations are:
[tex]7g + 3h = 26[/tex] --- (1)
[tex]4g + 5h = 28[/tex] --- (2)
Make g the subject in (2)
[tex]4g + 5h = 28[/tex]
[tex]4g = 28 - 5h[/tex]
Divide both sides by 4
[tex]g = \frac{1}{4}(28 - 5h)[/tex]
Substitute [tex]\frac{1}{4}(28 - 5h)[/tex] for g in (1)
[tex]7g + 3h = 26[/tex]
[tex]7(\frac{1}{4}(28 - 5h)) + 3h = 26[/tex]
[tex]\frac{7}{4}(28 - 5h) + 3h = 26[/tex]
Multiply through by 4
[tex]4 * \frac{7}{4}(28 - 5h) + 4*3h = 26*4[/tex]
[tex]7(28 - 5h) + 4*3h = 26*4[/tex]
Open bracket
[tex]196 - 35h + 12h = 104[/tex]
[tex]196 -23h = 104[/tex]
Collect Like Terms
[tex]-23h = 104-196[/tex]
[tex]-23h = -92[/tex]
Make h the subject
[tex]h = \frac{-92}{-23}[/tex]
[tex]h = \frac{92}{23}[/tex]
[tex]h = 4[/tex]
Substitute 4 for h in [tex]g = \frac{1}{4}(28 - 5h)[/tex]
[tex]g = \frac{1}{4}(28 - 5*4)[/tex]
[tex]g = \frac{1}{4}(28 - 20)[/tex]
[tex]g = \frac{1}{4}(8)[/tex]
[tex]g = 2[/tex]
This implies that:
1 goldfish = $2
1 hermit crab = $4
The cost of 6 goldfish and 4 hermit crabs is:
[tex]Cost = 6g + 4h[/tex]
[tex]Cost = 6*\$2 + 4*\$4[/tex]
[tex]Cost = \$12 + \$16[/tex]
[tex]Cost = \$28[/tex]
