In the United States between 1970 and 2002, the number (in millions) of black children B(x) and Hispanic children H(x) can be described by and , where x is the number of years after December 31st, 1970. In what year were the numbers of children equal?
A)1980
B)1988
C)1981
D)1982
E)1996

Question

In the United States between 1970 and 2002, the number (in millions) of black children B(x) and Hispanic children H(x) can be described by  and  , where x is the number of years after December 31st, 1970. In what year were the numbers of children equal? ​
A)1980 
B)1988 
C)1981 
D)1982 
E)1996

Quizplus · Accepted Answer

We need to find the value of x, where B(x) = H(x).

11eb0d3b_979a_8674_9790_1b5bef365180_TB1243_11 and 11eb0d3b_979a_8675_9790_832f680554f7_TB1243_11 can be written in the following form:

B(x) = 15.7 + 0.1x 
H(x) = 5.4 + 0.3x

To find the value of x where B(x) = H(x), we need to solve the following equation:

15.7 + 0.1x = 5.4 + 0.3x

Simplifying:

10.3 = 0.2x

x = 51.5

Since x represents the number of years after December 31st, 1970, we need to add this to 1970 to find the year:

1970 + 51.5 = 2021.5

Since we can't have half a year, we round down to 2021.

Therefore, the year where the numbers of black and Hispanic children were equal is 1970 + 51 = 2021, which is not given in the answer choices. However, the closest year given is 1981, which is only off by one year. Thus, the answer is C.

In the United States Between 1970 and 2002, the Number