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Question Number 44324 by Rio Michael last updated on 26/Sep/18

$$52a$$$$+35$$$$\mathrm{\_}\mathrm{\_}\mathrm{\_}theadditionontheleftisinbase6.finda.$$$$1001$$

Answered by MJS last updated on 27/Sep/18

$$\mathrm{in}\mathrm{base}6\mathrm{similar}\mathrm{to}\mathrm{what}\mathrm{we}\mathrm{learned}\mathrm{in}$$$$\mathrm{primary}\mathrm{school}:$$$$1001-0035=?$$$$5+2=11,\mathrm{write}2,\mathrm{keep}1\mathrm{in}\mathrm{mind}$$$$1001-0035=2$$$$3+1=4$$$$4+2=10,\mathrm{write}2,\mathrm{keep}1\mathrm{in}\mathrm{mind}$$$$1001-0035=22$$$$0+1=1$$$$1+5=10,\mathrm{write}5,\mathrm{keep}1\mathrm{in}\mathrm{mind}$$$$1001-35=522$$$$0+1=1$$$$1+0=1,\mathrm{so}{\mathrm{we}}^{\prime }\mathrm{re}\mathrm{ready}$$$$$$$$a=2$$

Answered by MrW3 last updated on 27/Sep/18

$${\left(52a\right)}_6=5\times 6^2+2\times 6^1+a\times 6^0=192+a$$$${\left(35\right)}_6=3\times 6^1+5\times 6^0=23$$$${\left(1001\right)}_6=1\times 6^3+0\times 6^2+0\times 6^1+1\times 6^0=217$$$$192+a+23=217$$$$\Rightarrow a=2$$

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