A childs ticket = $28 and an adult = $45
Total Cost to each family is the number of adult tickets bought multiplied by "x" PLUS the number of child tickets bought multiplied by "y"
Henson's equation = 3x + y = 163 Garcia's equation = 2x + 3y = 174
using the substitution method we need to express either x or y in terms of the other variable. In this example looking at the Henson equation it is very easy to express y in terms of x.
Rewrite the Henson equation to make y the subject y = 163 - 3x Substitute this value (163 - 3x) for "y" in the Garcia equation which now becomes
2x + 3(163 - 3x) = 174 Expand the bracket 2x + 489 - 9x = 174 -7x + 489 = 174 Add 7x and subtract 174 from both sides of the equation 315 = 7x 315/7 = x 45 = x An adult ticket costs $45 Substitute this back into the Henson equation 3 * 45 + y = 163 135 + y = 163 y = 163 - 135 = 28 A childs ticket costs $28
Check in the Garcia equation 2 * 45 + 3 * 28 = 90 + 84 = 174 = CORRECT
A childs ticket = $28 and an adult = $45
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Answer:
<h2>19 students</h2>
Step-by-step explanation:
We will use the set notation to solve this question.
let n(U) be the total number of students surveyed = 100
n(M) be the number of student that took math = 34
n(E) be the number of student that took English = 59
n(M∩E) be the number of student that took both classes= 12
n(M∪E)' be the number of student that took neither class = ?
Using the formula n(U) = n(M∪E) + n(M∪E)'
n(M∪E)' = n(U)-n(M∪E)
Before we can get the number of student that took neither class i.e n(M∪E)' we need to get n(M∪E).
n(M∪E) = n(M)+n(E)- n(M∩E)
n(M∪E) = 34+59-12
n(M∪E) = 81
Since n(M∪E)' = n(U)-n(M∪E);
n(M∪E)' = 100-81
n(M∪E)' = 19
<em>Hence 19 students took neither class as a freshmen.</em>
