You buy 3 shirts and 1 pair of pants for $32. Your friend buys 2 shirts and 3 pairs of pants for $40. How much did each item cost?
First let’s define a shirt as X and pants as Y!
In the first scenario, the equation will be 3X + Y =$32
In the second scenario, the equation will be 2X + 3Y = $40
Now because we have two different variables (X & Y) let’s solve for one of them (Ex: Y) to simplify the equations!
3X + Y= $32—> subtract 3X on both sides of the equation
-3X. - 3X
Net result: Y= 32- 3X
Now we can insert this into the second equation 2X + 3Y = $40 in order to solve for X variable
2X + 3(32-3X) = $40
2X + 96 - 9X = $40 —> simplify the equation
-7X + 96 = $40 —> substrate 96 from both sides
-7X = -56 —> divide both sides by -7
X= 8
Now reinsert 8= X into 3X + Y = $32
3(8) + Y = $32
24+ Y = $32 —> substract 24 from both sides
y = 8
ANSWER: X= 8, Y= 8
If I am wrong I am sorry >_<
Answer:
(-2,-7)
Step-by-step explanation:
x comes before Y
Answer:
225
Step-by-step explanation:
75/100×300=225
Answer:
the correct answer is 7/20
For this case we must simplify the following expression:
![\sqrt [3] {\frac {12x ^ 2} {16y}}](https://tex.z-dn.net/?f=%5Csqrt%20%5B3%5D%20%7B%5Cfrac%20%7B12x%20%5E%202%7D%20%7B16y%7D%7D)
We rewrite the expression as:
![\sqrt[3]{\frac{4(3x^2)}{4(4y)}}=\\\sqrt[3]{\frac{4(3x^2)}{4(4y)}}=\\\frac{\sqrt[3]{3x^2}}{\sqrt[3]{4y}}=](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B%5Cfrac%7B4%283x%5E2%29%7D%7B4%284y%29%7D%7D%3D%5C%5C%5Csqrt%5B3%5D%7B%5Cfrac%7B4%283x%5E2%29%7D%7B4%284y%29%7D%7D%3D%5C%5C%5Cfrac%7B%5Csqrt%5B3%5D%7B3x%5E2%7D%7D%7B%5Csqrt%5B3%5D%7B4y%7D%7D%3D)
We multiply the numerator and denominator by:
![(\sqrt[3]{4y})^2:\\\frac{\sqrt[3]{3x^2}*(\sqrt[3]{4y})^2}{\sqrt[3]{4y}*(\sqrt[3]{4y})^2}=](https://tex.z-dn.net/?f=%28%5Csqrt%5B3%5D%7B4y%7D%29%5E2%3A%5C%5C%5Cfrac%7B%5Csqrt%5B3%5D%7B3x%5E2%7D%2A%28%5Csqrt%5B3%5D%7B4y%7D%29%5E2%7D%7B%5Csqrt%5B3%5D%7B4y%7D%2A%28%5Csqrt%5B3%5D%7B4y%7D%29%5E2%7D%3D)
We use the rule of power
in the denominator:
![\frac{\sqrt[3]{3x^2}*(\sqrt[3]{4y})^2}{(\sqrt[3]{4y})^3}=\\\frac{\sqrt[3]{3x^2}*(\sqrt[3]{4y})^2}{4y}=](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%5B3%5D%7B3x%5E2%7D%2A%28%5Csqrt%5B3%5D%7B4y%7D%29%5E2%7D%7B%28%5Csqrt%5B3%5D%7B4y%7D%29%5E3%7D%3D%5C%5C%5Cfrac%7B%5Csqrt%5B3%5D%7B3x%5E2%7D%2A%28%5Csqrt%5B3%5D%7B4y%7D%29%5E2%7D%7B4y%7D%3D)
Move the exponent within the radical:
![\frac{\sqrt[3]{3x^2}*(\sqrt[3]{16y^2}}{4y}=\\\frac{\sqrt[3]{3x^2}*(\sqrt[3]{2^3*(2y^2)}}{4y}=](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%5B3%5D%7B3x%5E2%7D%2A%28%5Csqrt%5B3%5D%7B16y%5E2%7D%7D%7B4y%7D%3D%5C%5C%5Cfrac%7B%5Csqrt%5B3%5D%7B3x%5E2%7D%2A%28%5Csqrt%5B3%5D%7B2%5E3%2A%282y%5E2%29%7D%7D%7B4y%7D%3D)
![\frac{2\sqrt[3]{3x^2}*(\sqrt[3]{(2y^2)}}{4y}=\\\frac{2\sqrt[3]{6x^2*y^2}}{4y}=](https://tex.z-dn.net/?f=%5Cfrac%7B2%5Csqrt%5B3%5D%7B3x%5E2%7D%2A%28%5Csqrt%5B3%5D%7B%282y%5E2%29%7D%7D%7B4y%7D%3D%5C%5C%5Cfrac%7B2%5Csqrt%5B3%5D%7B6x%5E2%2Ay%5E2%7D%7D%7B4y%7D%3D)
![\frac{\sqrt[3]{6x^2*y^2}}{2y}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%5B3%5D%7B6x%5E2%2Ay%5E2%7D%7D%7B2y%7D)
Answer:
