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The ratio of ingredients $X$ and $Y$ is $\\var{x}: \\var{y}$.

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This means that for every $\\var{x}$g of $X$, we need $\\var{y}$g of $Y$. You could imagine organising your ingredients so that you put ingredient $X$ into small bags containing $\\var{x}$g and ingredient $Y$ into small bags containing $\\var{y}$g.

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For each 'batch' of cake mixture you will need one bag of each of the secret ingredients, which will weigh a total of $\\simplify { {x} + {y} }$g in total.

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For a total of $\\simplify{{t} *({x}+{y})}$g of secret ingredients we will need $\\var{t}$ batches.

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This means we will need $\\var{t} \\times \\var{whichone}=\\var{t*whichone}$g of ingredient {this}.

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A cake recipe includes two secret ingredients $X$ and $Y$. These must be added so that the ratio $X:Y$ is $\\var{x}:\\var{y}$.

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The combined weight of the two secret ingredients is $\\simplify{{t}*({x}+{y})}$g.

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How much of ingredient {this} should be added?

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[[0]]g

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Solve the following ratio problem.

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Given the ratio of ingredients and the total amount of ingredients work out how much of one of the ingredients is needed.

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A piece of $\\var{material}$ $\\var{lent}$ cm long is cut into three pieces in the ratio of $\\var{numberone}$ to $\\var{numbertwo}$ to $\\var{numberthree}$. Determine the lengths of the three pieces.

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[[0]]cm

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[[1]]cm

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[[2]]cm

Imagine that the $\\var{material}$ is divided into $\\var{numberone}$ + $\\var{numbertwo}$ +$\\var{numberthree}$ pieces. The first piece should be $\\var{numberone}$ times its length. The second piece should be $\\var{numbertwo}$ times this length. The third piece should be $\\var{numberthree}$ times this length.

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Double check: When you add up your pieces they should add to $\\var{lent}$.

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Divide $\\var{total}$ in the ratio $\\var{numberone1}$:$\\var{numbertwo1}$:$\\var{numberfour}$.

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[[0]]

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[[1]]

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[[2]]

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Divide $\\var{total}$  into $\\var{numberone1}$  + $\\var{numbertwo1}$  + $\\var{numberfour}$ parts. Each of these parts contain $\\var{k}$.

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Find $k \\times \\var{numberone}$

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Find $k \\times \\var{numbertwo}$

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Find $k \\times \\var{numberfour}$

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To double check, add these results together. You should get $\\var{total}$.

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Divide €$\\var{money}$ in the ratio $\\var{ratioab[0]}:\\var{ratioab[1]}:\\var{ratioc}$

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(Calculate to 2 decimal place!!)

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€[[0]] : €[[1]] : €[[2]]

Just as before, add all parts together and divide by this.

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Ratio Questions

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Part 1:

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Add the ratio numbers and then divide the length by the summed total

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$\\frac{\\var{lent}}{\\var{summ}}$

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Then multiply each peice by the ratio length

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$\\var{numberone} \\times \\var{ratio}$

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$\\var{numbertwo} \\times \\var{ratio}$

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$\\var{numberthree} \\times \\var{ratio}$

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Part 2:

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Use the same method as in part 1

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$\\frac{\\var{total}}{(\\var{numberone1}+\\var{numbertwo1}+\\var{numberfour})}$

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$\\var{numberone} \\times \\var{k}$

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$\\var{numbertwo} \\times \\var{k}$

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$\\var{numberfour} \\times \\var{k}$

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Part 4:

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$(\\frac{\\var{money}}{(\\var{ratioab[0]} + \\var{ratioab[1]} + \\var{ratioc})}) \\times \\var{ratioab[0]} = \\var{ans31}$

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$(\\frac{\\var{money}}{(\\var{ratioab[0]} + \\var{ratioab[1]} + \\var{ratioc})}) \\times \\var{ratioab[1]} = \\var{ans32}$

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$(\\frac{\\var{money}}{(\\var{ratioab[0]} + \\var{ratioab[1]} + \\var{ratioc})}) \\times \\var{ratioc} = \\var{ans33}$

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## Solve the following to the nearest whole number:

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