Answer:
Smaller Amount =$206
Larger Amount =$309
Step-by-step explanation:
Let the total amount of money =x
The money will be divided in the ratio 2:3
Total Number of Shares =2+3=5
Therefore:
Smaller Amount ![=\dfrac25x](https://tex.z-dn.net/?f=%3D%5Cdfrac25x)
Larger Amount![=\dfrac35x](https://tex.z-dn.net/?f=%3D%5Cdfrac35x)
Four times the smaller amount is one hundred three dollars less than three times the larger amount.
Therefore:
![3$ X\dfrac35x=4$ X \dfrac25x + 103\\\dfrac{9x}{5}=\dfrac{8x}{5}+103\\$Collect like terms\\\dfrac{9x}{5}-\dfrac{8x}{5}=103\\\dfrac{x}{5}=103\\$Cross multiply\\x=103*5\\Amount of money to be shared, x=\$515](https://tex.z-dn.net/?f=3%24%20X%5Cdfrac35x%3D4%24%20X%20%5Cdfrac25x%20%2B%20103%5C%5C%5Cdfrac%7B9x%7D%7B5%7D%3D%5Cdfrac%7B8x%7D%7B5%7D%2B103%5C%5C%24Collect%20like%20terms%5C%5C%5Cdfrac%7B9x%7D%7B5%7D-%5Cdfrac%7B8x%7D%7B5%7D%3D103%5C%5C%5Cdfrac%7Bx%7D%7B5%7D%3D103%5C%5C%24Cross%20multiply%5C%5Cx%3D103%2A5%5C%5CAmount%20of%20money%20to%20be%20shared%2C%20x%3D%5C%24515)
Therefore:
Smaller Amount ![=\dfrac25$ X 515 =\$206\\](https://tex.z-dn.net/?f=%3D%5Cdfrac25%24%20X%20515%20%3D%5C%24206%5C%5C)
Larger Amount![=\dfrac35$ X 515 =\$309](https://tex.z-dn.net/?f=%3D%5Cdfrac35%24%20X%20515%20%3D%5C%24309)
Why did you delete my question? I answered it correctly.
Infinity is not a real/rational number.
Answer:
7
Step-by-step explanation:
the median is the number in the middle of a sorted array
here it has 10 numbers, so the median will be the average of the 5th and the 6th number
the 5th number is 7 and the 6th number is 7
the average is (7+7)/2 = 7
so the median is 7
Answer:
y ≈ 240.3 ft
Step-by-step explanation:
The mnemonic SOH CAH TOA reminds you that the relation between an angle and the sides adjacent and opposite is ...
Tan = Opposite/Adjacent
In this triangle, the interior angle at lower right is the same as the one marked at upper left: 31°. y is the side opposite that angle, and 400 ft is the side adjacent. Then the relation is ...
tan(31°) = y/(400 ft)
Multiplying by 400 ft gives ...
y = (400 ft)·tan(31°) ≈ 240.3 ft
_____
The triangle interior angle at lower right and the angle marked 31° are "alternate interior angles" relative to the transversal marked x and the (parallel) horizontal lines in the figure. Alternate interior angles always have the same measure.
In geometry problems like this one, it means the angle of elevation (above the horizontal) is equal to the angle of depression (below the horizontal).
Answer:
Jeff's ribbon is,
feet long
Step-by-step explanation:
Let J represents the length of Jeff ribbon and B represents the length of Bill ribbon.
As per the condition:
Jeff's ribbon is 3/7 the length of Bill's ribbon.
⇒
......[1]
It is also given that: if both ribbons combined are 2 feet long.
⇒J + B = 2 ......[2]
Substitute the equation [1] into [2] we get;
![\frac{3}{7}B+B = 2](https://tex.z-dn.net/?f=%5Cfrac%7B3%7D%7B7%7DB%2BB%20%3D%202)
Simplify:
![\frac{10}{7}B = 2](https://tex.z-dn.net/?f=%5Cfrac%7B10%7D%7B7%7DB%20%3D%202)
Multiply both sides by
we get;
ribbons
Substitute the value of B in equation [1] we have;
feet
Therefore, Jeff's ribbon is,
feet long