the question in English
Juan has blue cubes with a 55 mm edge and red cubes with a 45 mm edge. He stacks them in two columns, one of each color; he wants the two columns to be the same height. How many cubes does he need, as a minimum, of each color?
Let
x---------> the number of blue cubes
y--------> the number of red cubes
we know that
Juan wants that the two columns to be the same height
so
![55x=45y](https://tex.z-dn.net/?f=55x%3D45y)
solve for y
![y=\frac{55}{45}x](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B55%7D%7B45%7Dx)
I proceed to calculate a table, assuming values of x to calculate the value of y. When the values of x and y are whole numbers, I will have found the solution.
the table in the attached figure
therefore
<u>the answer is</u>
9 blue cubes
11 red cubes
Answer:
I think the answer would be 33. I am not exactly sure though.
Answer:
![-\frac{16}{17}\\-0.94117](https://tex.z-dn.net/?f=-%5Cfrac%7B16%7D%7B17%7D%5C%5C-0.94117)
Step-by-step explanation:
![\frac{-\frac{1}{2}}{\frac{2\left(9+3\right)-4-3}{4\left(8\right)}}\\\mathrm{Remove\:parentheses}:\quad \left(a\right)=a\\=\frac{-\frac{1}{2}}{\frac{2\left(9+3\right)-4-3}{4\cdot \:8}}\\\frac{2\left(9+3\right)-4-3}{4\cdot \:8}=\frac{17}{32}\\\frac{2\left(9+3\right)-4-3}{4\cdot \:8}\\2\left(9+3\right)-4-3=17\\2\left(9+3\right)-4-3\\2\left(9+3\right)=24\\2\left(9+3\right)\\\mathrm{Add\:the\:numbers:}\:9+3=12\\=2\cdot \:12\\\mathrm{Multiply\:the\:numbers:}\:2\cdot \:12=24\\=24-4-3](https://tex.z-dn.net/?f=%5Cfrac%7B-%5Cfrac%7B1%7D%7B2%7D%7D%7B%5Cfrac%7B2%5Cleft%289%2B3%5Cright%29-4-3%7D%7B4%5Cleft%288%5Cright%29%7D%7D%5C%5C%5Cmathrm%7BRemove%5C%3Aparentheses%7D%3A%5Cquad%20%5Cleft%28a%5Cright%29%3Da%5C%5C%3D%5Cfrac%7B-%5Cfrac%7B1%7D%7B2%7D%7D%7B%5Cfrac%7B2%5Cleft%289%2B3%5Cright%29-4-3%7D%7B4%5Ccdot%20%5C%3A8%7D%7D%5C%5C%5Cfrac%7B2%5Cleft%289%2B3%5Cright%29-4-3%7D%7B4%5Ccdot%20%5C%3A8%7D%3D%5Cfrac%7B17%7D%7B32%7D%5C%5C%5Cfrac%7B2%5Cleft%289%2B3%5Cright%29-4-3%7D%7B4%5Ccdot%20%5C%3A8%7D%5C%5C2%5Cleft%289%2B3%5Cright%29-4-3%3D17%5C%5C2%5Cleft%289%2B3%5Cright%29-4-3%5C%5C2%5Cleft%289%2B3%5Cright%29%3D24%5C%5C2%5Cleft%289%2B3%5Cright%29%5C%5C%5Cmathrm%7BAdd%5C%3Athe%5C%3Anumbers%3A%7D%5C%3A9%2B3%3D12%5C%5C%3D2%5Ccdot%20%5C%3A12%5C%5C%5Cmathrm%7BMultiply%5C%3Athe%5C%3Anumbers%3A%7D%5C%3A2%5Ccdot%20%5C%3A12%3D24%5C%5C%3D24-4-3)
![\mathrm{Subtract\:the\:numbers:}\:24-4-3=17\\=\frac{17}{4\cdot \:8}\\\mathrm{Multiply\:the\:numbers:}\:4\cdot \:8=32\\=\frac{17}{32}\\\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{-a}{b}=-\frac{a}{b}\\=-\frac{\frac{1}{2}}{\frac{17}{32}}\\\mathrm{Divide\:fractions}:\quad \frac{\frac{a}{b}}{\frac{c}{d}}=\frac{a\cdot \:d}{b\cdot \:c}\\=-\frac{1\cdot \:32}{2\cdot \:17}\\Refine\\=-\frac{32}{2\cdot \:17}\\\mathrm{Multiply\:the\:numbers:}\:2\cdot \:17=34\\=-\frac{32}{34}](https://tex.z-dn.net/?f=%5Cmathrm%7BSubtract%5C%3Athe%5C%3Anumbers%3A%7D%5C%3A24-4-3%3D17%5C%5C%3D%5Cfrac%7B17%7D%7B4%5Ccdot%20%5C%3A8%7D%5C%5C%5Cmathrm%7BMultiply%5C%3Athe%5C%3Anumbers%3A%7D%5C%3A4%5Ccdot%20%5C%3A8%3D32%5C%5C%3D%5Cfrac%7B17%7D%7B32%7D%5C%5C%5Cmathrm%7BApply%5C%3Athe%5C%3Afraction%5C%3Arule%7D%3A%5Cquad%20%5Cfrac%7B-a%7D%7Bb%7D%3D-%5Cfrac%7Ba%7D%7Bb%7D%5C%5C%3D-%5Cfrac%7B%5Cfrac%7B1%7D%7B2%7D%7D%7B%5Cfrac%7B17%7D%7B32%7D%7D%5C%5C%5Cmathrm%7BDivide%5C%3Afractions%7D%3A%5Cquad%20%5Cfrac%7B%5Cfrac%7Ba%7D%7Bb%7D%7D%7B%5Cfrac%7Bc%7D%7Bd%7D%7D%3D%5Cfrac%7Ba%5Ccdot%20%5C%3Ad%7D%7Bb%5Ccdot%20%5C%3Ac%7D%5C%5C%3D-%5Cfrac%7B1%5Ccdot%20%5C%3A32%7D%7B2%5Ccdot%20%5C%3A17%7D%5C%5CRefine%5C%5C%3D-%5Cfrac%7B32%7D%7B2%5Ccdot%20%5C%3A17%7D%5C%5C%5Cmathrm%7BMultiply%5C%3Athe%5C%3Anumbers%3A%7D%5C%3A2%5Ccdot%20%5C%3A17%3D34%5C%5C%3D-%5Cfrac%7B32%7D%7B34%7D)
![\mathrm{Cancel\:the\:common\:factor:}\:2\\=-\frac{16}{17}\\\mathrm{Decimal:\quad }\:-0.94117](https://tex.z-dn.net/?f=%5Cmathrm%7BCancel%5C%3Athe%5C%3Acommon%5C%3Afactor%3A%7D%5C%3A2%5C%5C%3D-%5Cfrac%7B16%7D%7B17%7D%5C%5C%5Cmathrm%7BDecimal%3A%5Cquad%20%7D%5C%3A-0.94117)
The nearest whole number to <span>17 5/8 would be 18.</span>