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77julia77 [94]
2 years ago
8

Solve each of these equations. Explain or show your reasoning.

Mathematics
1 answer:
Svetlanka [38]2 years ago
4 0

1.

2(x+5)=3x+1 \\2x+10=3x+1 \\-x=-9 \\x=9

2.

3y-4=6-2y \\5y=10 \\y=2

3.

3(n+2)=9(6-n) \\3n+6=54-9n \\12n=48 \\n=\frac{48}{12}=4

Hope this helps.

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A bank loaned out $68,000, part of it at the rate of 13% per year and the rest at a rate of 5%per year. If the interest received
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Answer: $31000 was loaned at 13%.

Step-by-step explanation:

Let x represent the amount loaned out at 13% interest rate.

Let y represent the amount loaned out at 5% interest rate.

The bank loaned out $68,000, part of it at the rate of 13% per year and the rest at a rate of 5%per year. It means that

x + y = 68000

The interest received made from $x in one year is

13/100 × x = 0.13x

The interest received made from $y in one year is

5/100 × x = 0.05y

If the interest received was $5880, it means that

0.13x + 0.05y = 5880- - - - - - - - - 1

Substituting x = 68000 - y into equation 1, it becomes

0.13(68000 - y) + 0.05y = 5880

8840 - 0.13y + 0.05y = 5880

- 0.13y + 0.05y = 5880 - 8840

- 0.08y = - 2960

y = - 2960/- 0.08

y = 37000

x = 68000 - y = 68000 - 37000

x = $31000

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