Mathematics, 29.12.2021 14:00 johnathan1104
Two positive numbers are in the ratio 2 : 3. Find the numbers if (a) their sum is 55 and (b) their product is 384.
Answers: 1
![\stackrel{\textit{in the ratio of 2 to 3}}{a~:~b\qquad \qquad 2:3}\qquad \qquad \implies \qquad \cfrac{a}{b}=\cfrac{2}{3}\implies \cfrac{3a}{2}=b \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{their sum is 55}}{a + b = 55}\implies a + \cfrac{3a}{2}=55\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{2}}{2\left( a + \cfrac{3a}{2} \right)=2(55)} \\\\\\ 2a+3a=110\implies 5a=110\implies a = \cfrac{110}{2}\implies \boxed{a = 22}](/tpl/images/2606/9807/cc72b.png)
![\stackrel{\textit{we know that}}{\cfrac{3a}{2}=b}\implies \cfrac{3(22)}{2}=b\implies \boxed{33=b} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{their product is 384}}{ab=384}\implies a\left( \cfrac{3a}{2} \right)=384\implies \cfrac{3a^2}{2}=384\implies 3a^2=768 \\\\\\ a^2=\cfrac{768}{3}\implies a^2=256\implies a=\sqrt{256}\implies \boxed{a=16} \\\\\\ \stackrel{\textit{we know that}}{\cfrac{3a}{2}=b}\implies \cfrac{3(16)}{2}=b\implies \boxed{24=b}](/tpl/images/2606/9807/de44c.png)
Another question on Mathematics
Mathematics, 21.06.2019 19:30
Fa bus driver leaves her first stop by 7: 00 a.m., her route will take less than 37 minutes. if she leaves after 7: 00 a.m., she estimates that the same route will take no less than 42 minutes. which inequality represents the time it takes to drive the route, r?
Answers: 3
Mathematics, 21.06.2019 19:30
Mr. brettler is hanging up a 5-foot tall rectangular welcome sign in the gym. he has drawn a sketch on a coordinate grid. he has the lower vertices of the sign at (9, –3) and (–6, –3). where would the upper vertices be on the grid?
Answers: 1
Mathematics, 21.06.2019 20:30
On a cm grid, point p has coordinates (3,-1) and point q has coordinates (-5,6) calculate the shortest distance between p and q give your answer to 1 decimal place
Answers: 2
Mathematics, 21.06.2019 21:00
Rewrite the following quadratic functions in intercept or factored form. show your work. y = x^2 + 7x + 10
Answers: 2
You know the right answer?
Two positive numbers are in the ratio 2 : 3. Find the numbers if (a) their sum is 55 and (b) their p...
Questions
Mathematics, 06.12.2019 02:31
History, 06.12.2019 02:31
World Languages, 06.12.2019 02:31
Biology, 06.12.2019 02:31
History, 06.12.2019 02:31
History, 06.12.2019 02:31
Mathematics, 06.12.2019 02:31
Mathematics, 06.12.2019 02:31
Mathematics, 06.12.2019 02:31
Mathematics, 06.12.2019 02:31
Mathematics, 06.12.2019 02:31
History, 06.12.2019 02:31
Mathematics, 06.12.2019 02:31
