Question

The bar graph shows the percentage of households in 1988 and 2008 with an interfaith marriage andthe percentage of households in which a person of faith is married to someone with no religion. Theformula 1= x+56 models the percentage of households with an interfaith marriage, 1, x years after1988. The formula N=-x+36 models the percentage of households in which a person of faith ismarried to someone with no religion, N. x years after 1988. Use the models to complete parts (a)through (c) below.a. In which years will more than 67% of households have an interfaith marriage?More than 67% of households have an interfaith marriage in the years afterPct of Households60-66150-40-30-20-10-061Interfaith19982008 QFaith No ReligionG

Answer 1

We can see from the question that:

1. The next formula models the percentage of households with interfaith marriage, I, after 1988:

`I=(1)/(4)x+56`

2. The next formula models the percentage of households in which a person of faith is married to someone with no religion, N, x years after 1988:

`N=(1)/(4)x+36`

And we need to find in which years more than 67% of households have had an interfaith marriage.

3. Then to find it, we can use the given formula for interfaith marriage as follows:

`\begin{gathered} I=(1)/(4)x+56 \\ \\ 67=(1)/(4)x+56 \\ \end{gathered}`

4. And now, we have to solve the equation for x as follows:

`\begin{gathered} 67-56=(1)/(4)x+56-56 \\ \\ 11=(1)/(4)x \\ \\ \end{gathered}`

5. Now, we need to multiply by 4 to both sides of the equation as follows:

`\begin{gathered} 4(11)=4((1)/(4)x) \\ \\ 44=x \\ \\ x=44 \end{gathered}`

6. Since x is the number of years after 1988, then we need to sum 44 to 1988 as follows:

`1988+44=2032`

Therefore, we can conclude that more than 67% of households have an interfaith marriage in the year after 2032 (because in 2032 will be 67%).