Question

In which of the following categories is the range of amounts the families spend the highest?HousingFoodChildcareTransportationInsuranceOther NeedsTaxes

Answer 1

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Define the formula for range

`\begin{gathered} \text{Range}=\text{Maximum-Minimum} \\ \text{Range}=Highest\text{ Value-Lowest Value} \end{gathered}`

STEP 2: Explain how to calculate the values from a pie chart

`Value=percentage* Total`

STEP 3: Calculate the housings for each of the THREE families

`\begin{gathered} \text{Housing for }Family\text{ A} \\ (19)/(100)*5400=19*54=\text{\$}1026\text{ } \\ \\ \text{Housing for Family B} \\ (16)/(100)*4675=(16*4675)/(100)=\text{\$}748\text{ } \\ \\ \text{Housing for Family C} \\ (14)/(100)*6675=(14*6675)/(100)=\text{\$}934.50\text{ } \\ \\ \text{Range}=\text{\$}1026-\text{\$}748=\text{\$}278 \end{gathered}`

STEP 4: Calculate theRANGE for food for each of the THREE families

`\begin{gathered} \text{Food for Family A} \\ (14)/(100)*5400=14*54=\text{\$}756\text{ } \\ \\ \text{Food for Family B} \\ (16)/(100)*4675=(16*4675)/(100)=\text{\$}654.50\text{ } \\ \\ \text{Food for Family C} \\ (11)/(100)*6675=(11*6675)/(100)=\text{\$}734.25\text{ } \\ \\ \text{Range}=\text{\$}756-\text{\$}654.50=\text{\$}101.50 \end{gathered}`

STEP 5: Calculate the RANGE for Childcare for each of the THREE families

`\begin{gathered} \text{Childcare for Family A} \\ (18)/(100)*5400=972 \\ \text{Childcare for Family B} \\ (18)/(100)*4675=841.5 \\ \text{Childcare for Family C} \\ (30)/(100)*6675=(30*6675)/(100)=2002.5 \\ \\ \text{Range}=2002.5-841.5=\text{\$}1161\text{ } \end{gathered}`

STEP 6: Calculate the RANGE for Transportation for each of the THREE families

`\begin{gathered} \text{Transportation for Family A} \\ (11)/(100)*5400=11*54=\text{\$}594 \\ \text{Transportation for Family B} \\ (13)/(100)*4675=(13*4675)/(100)=\text{\$}607.75\text{ } \\ \text{Transportation for Family C} \\ (9)/(100)*6675=(9*6675)/(100)=\text{\$}600.75 \\ \\ \text{Range}=\text{\$}607.75-\text{\$}594=\text{\$}13.75 \end{gathered}`

STEP 7: Calculate the RANGE for Insurance for each of the THREE families

`\begin{gathered} \text{Insurance for Family A} \\ (23)/(100)*5400=23*54=\text{\$}1242 \\ \text{Insurance for Family B} \\ (28)/(100)*4675=(28*4675)/(100)=\text{\$}1309 \\ \text{Insurance for Family C} \\ (20)/(100)*6675=(20*6675)/(100)=\text{\$}1335 \\ \\ \text{Range}=\text{\$}1335-\text{\$}1242=\text{\$}93 \end{gathered}`

STEP 8: Calculate the RANGE for other needs for each of the THREE families

`\begin{gathered} \text{Other n}eeds\text{ for Family A} \\ (9)/(100)*5400=9*54=\text{\$}486 \\ \text{Other n}eeds\text{ for Family B} \\ (7)/(100)*4675=(7*4675)/(100)=\text{\$}327.25 \\ \text{Other n}eeds\text{ for Family C} \\ (6)/(100)*6675=(6*6675)/(100)=\text{\$}400.5 \\ \\ \text{Range}=\text{\$}486-\text{\$}327.25=\text{\$}158.75 \end{gathered}`

STEP 9: Calculate the RANGE for Taxes for each of the THREE families

`\begin{gathered} \text{Taxes for Family A} \\ (5)/(100)*5400=5*54=\text{\$}270 \\ \text{Taxes for Family B} \\ (2)/(100)*4675=(2*4675)/(100)=\text{\$}93.50 \\ \text{Taxes for Family C} \\ (10)/(100)*6675=(10*6675)/(100)=\text{\$}667.50\text{ } \\ \\ \text{Range}=\text{\$}667.50-\text{\$}93.50=\text{\$}574 \end{gathered}`

It can be seen from the steps above that Childcare category has a range of $1161.00 hence this is the category with the highest range of amounts.

ANSWER: Childcare category