Topic $5$: Ratios and rates Test A $15$ A spinner with $3$ sections is to be made from a circular piece of cardboard. The $3$ angles are in the ratio $\backslash (1$: $2$: $3\backslash ).$ What is the magnitude of each angle? COMMUNICATING, REASONING AND PROBLEM SOLVING $16$ Joanna and John contributed $\backslash (\backslash$$ $2000\backslash )$ and $\backslash (\backslash$$ $3000\backslash )$ respectively, when starting up a new company. Joanna states that John should, therefore, receive $\backslash (\backslash$$ $1000\backslash )$ more of the profits than she. Is Joanna correct? Explain your answer. $17$ a If the gradient of KL is $1,$ describe the relationship between $\backslash ($ k $\backslash )$ and $\backslash ($ l $\backslash ).$ b If the gradient of KL is $2,$ describe the relationship between $\backslash ($ k $\backslash )$ and $\backslash ($ l $\backslash ).18$ If two similar rectangles have their sides in the ratio $\backslash (1$: $2\backslash ),$ find the ratio describing the relationship between their areas. Explain your working. $19$ a Which is the greater ratio: $\backslash (5$: $6\backslash )$ or $\backslash (3$: $4\backslash )?$ b If $\backslash (\backslash$frac$\{4\}\{7\}>\backslash$frac$\{$x$\}\{8\}\backslash ),$ find a range of values that could be $\backslash ($ x $\backslash ),$ if $\backslash ($ x $\backslash )$ is an integer. $20$ Grace can wash $2$ dishes per minute. Her brother Phil can wash $3$ dishes per minute. Find the total number of dishes Grace and Phil can wash in $30$ minutes?