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Vladimir79 [104]
2 years ago
9

A credit union loaned out $50,000, part at an annual rate of 6% and the rest at an annual rate of 12% . The collected combined i

nterest was $3,600 that year. How much did the credit union loan out at each rate?
Mathematics
1 answer:
Natasha_Volkova [10]2 years ago
5 0

Answer: the credit union loaned out $40000 at 6% and $10000 at 12%

Step-by-step explanation:

Let x represent the amount that the

credit union loaned out at the annual rate of 6%.

Let y represent the amount that the

credit union loaned out at the annual rate of 12%.

credit union loaned out $50,000, part at an annual rate of 6% and the rest at an annual rate of 12%. It means that

x + y = 50000

The interest on $x after 1 year would be

6/100 × x = 0.06x

The interest on $y after 1 year would be

12/100 × y = 0.12y

The collected combined interest was $3,600 that year. It means that

0.06x + 0.12y = 3600- - - - - - - - - 1

Substituting x = 50000 - y into equation 1, it becomes

0.06(50000 - y) + 0.12y = 3600

3000 - 0.06y + 0.12y = 3600

- 0.06y + 0.12y = 3600 - 3000

0.06y = 600

y = 600/0.06

y = $10000

x = 50000 - y = 50000 - 10000

x = $40000

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⠀

Explanation :

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{ \longrightarrow \qquad\pmb {\boldsymbol{ Volume_{(cylinder)} = \pi {r}^{2} h \: }}}

Where,

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Substituting the values in the formula :

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{ \longrightarrow \qquad{ \ {  \sf{ Volume_{(cylinder)} \it {= 3.14 \times ({4})^{2} \times 6 \: }}}}}

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{ \longrightarrow \qquad{ \ {  \sf{ Volume_{(cylinder)} \it {= 3.14 \times 16\times 6 \: }}}}}

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{ \longrightarrow \qquad{ \ {  \sf{ Volume_{(cylinder)} \it {= 3.14 \times 96 \: }}}}}

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{ \longrightarrow \qquad{ \ {  \it{ \pmb{ Volume_{(cylinder)}  {= 301.44 \: }}}}}}

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