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29.04.2021 •

Mathematics

Caleb invested $6,200 in an account paying an interest rate of 7 1/2% compounded quarterly. Sophie invested $6,200 in an account paying an interest rate of 7 7/8%
compounded monthly. To the nearest dollar, how much money would Sophie have in
her account when Caleb's money has doubled in value?

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Ответ:

peno211

04.07.2020

Mathematics

Given:

The ratio of the measures of the three sides of a triangle is $\dfrac{1}{4}:\dfrac{1}{3}:\dfrac{1}{6}$ .

Its perimeter is 31.4 centimeters

To find:

The shortest side of the triangle.

Solution:

Let the measures of the three sides of a triangle are $\dfrac{1}{4}x,\dfrac{1}{3}x,\dfrac{1}{6}x$ respectively (in cm).

Its perimeter is 31.4 centimeters.

$\dfrac{1}{4}x+\dfrac{1}{3}x+\dfrac{1}{6}x=31.4$

$\dfrac{3x+4x+2x}{12}=31.4$

$\dfrac{9x}{12}=31.4$

$\dfrac{3x}{4}=31.4$

On further simplification, we get

$3x=4\times 31.4$

3x=125.6

Divide both sides by 3.

$x=\dfrac{125.6}{3}$

x=41.867

Now, the sides of triangle are

$\dfrac{1}{4}(41.867)=10.467$

$\dfrac{1}{3}(41.867)=13.956$

$\dfrac{1}{6}(41.867)=6.978$

Therefore, the length of the shortest side is 6.978 cm.

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Caleb invested $6,200 in an account paying an interest rate of 7 1/2% compounded quarterly. Sophie invested $6,200 in an account paying an interest rate of 7 7/8% compounded monthly. To the nearest dollar, how much money would Sophie have in her account when Caleb's money has doubled in value?