Question

1. \\(\frac{3}{10} = \frac{9}{10x}\\) 4) \\(\frac{x}{3} = \frac{10}{2}\\) 5) \\(\frac{2}{7} = \frac{7}{k + 3}\\) 6) \\(\frac{3}{x + 3} = \frac{8}{2}\\) 7) \\(\frac{3}{x + 10} = \frac{2}{x}\\) 8) \\(\frac{7}{n} = \frac{8}{n + 10}\\) 1) the ratio of girls to boys in mrs. whites class is 3:2. if there are 12 boys, how many girls are in the classroom? 2) andrew bought 32 kiwi fruits for $16. how many kiwi fruits can he buy if he has $4 now? 3) 15 candy bars weigh 26 ounces. what is the weight of 35 candy bars?

Explanation:

Problem 3: $\boldsymbol{\frac{3}{10}=\frac{9}{10x}}$

Step1: Cross - multiply

We know that if $\frac{a}{b}=\frac{c}{d}$, then $a\times d = b\times c$. So for $\frac{3}{10}=\frac{9}{10x}$, we have $3\times10x=10\times9$.

Step2: Simplify the equation

Simplify both sides: $30x = 90$.

Step3: Solve for $x$

Divide both sides by 30: $x=\frac{90}{30}=3$.

Step1: Cross - multiply

Using the cross - multiplication rule $\frac{a}{b}=\frac{c}{d}\Rightarrow a\times d=b\times c$, we get $x\times2 = 3\times10$.

Step2: Simplify and solve for $x$

Simplify the right - hand side: $2x = 30$. Then divide both sides by 2: $x=\frac{30}{2}=15$.

Step1: Cross - multiply

Applying cross - multiplication, we have $2\times(k + 3)=7\times7$.

Step2: Expand and simplify

Expand the left - hand side: $2k+6 = 49$.

Step3: Solve for $k$

Subtract 6 from both sides: $2k=49 - 6=43$. Then divide both sides by 2: $k=\frac{43}{2}=21.5$.

Answer:

$x = 3$

Problem 4: $\boldsymbol{\frac{x}{3}=\frac{10}{2}}$