Question

the 435 members of the united states house of representatives are debating two laws. the number of members who support each of the laws is shown in the venn diagram. how many members of the u.s. house of representatives are supporting only law #2? members

Explanation:

Step1: Recall total - members formula

The total number of members is the sum of those who support only Law #1, only Law #2, both laws, and neither law. Let \(x\) be the number of members who support only Law #2. We know that the total number of members \(N = 435\), the number of members who support neither law \(n = 155\), the number of members who support only Law #1 \(a=85\), and the number of members who support both laws \(b = 135\). So \(N=n + a + b+x\).

Step2: Rearrange the formula to solve for \(x\)

We can rewrite the formula as \(x=N - n - a - b\). Substitute \(N = 435\), \(n = 155\), \(a = 85\), and \(b = 135\) into the formula.
\[x=435-155 - 85-135\]
\[x=(435-(155 + 85+135))\]
\[x=435 - 375\]
\[x = 60\]

Answer:

60