Whole numbers<span><span>\greenD{\text{Whole numbers}}Whole numbers</span>start color greenD, W, h, o, l, e, space, n, u, m, b, e, r, s, end color greenD</span> are numbers that do not need to be represented with a fraction or decimal. Also, whole numbers cannot be negative. In other words, whole numbers are the counting numbers and zero.Examples of whole numbers:<span><span>4, 952, 0, 73<span>4,952,0,73</span></span>4, comma, 952, comma, 0, comma, 73</span>Integers<span><span>\blueD{\text{Integers}}Integers</span>start color blueD, I, n, t, e, g, e, r, s, end color blueD</span> are whole numbers and their opposites. Therefore, integers can be negative.Examples of integers:<span><span>12, 0, -9, -810<span>12,0,−9,−810</span></span>12, comma, 0, comma, minus, 9, comma, minus, 810</span>Rational numbers<span><span>\purpleD{\text{Rational numbers}}Rational numbers</span>start color purpleD, R, a, t, i, o, n, a, l, space, n, u, m, b, e, r, s, end color purpleD</span> are numbers that can be expressed as a fraction of two integers.Examples of rational numbers:<span><span>44, 0.\overline{12}, -\dfrac{18}5,\sqrt{36}<span>44,0.<span><span> <span>12</span></span> <span> </span></span>,−<span><span> 5</span> <span> <span>18</span></span><span> </span></span>,<span>√<span><span> <span>36</span></span> <span> </span></span></span></span></span>44, comma, 0, point, start overline, 12, end overline, comma, minus, start fraction, 18, divided by, 5, end fraction, comma, square root of, 36, end square root</span>Irrational numbers<span><span>\maroonD{\text{Irrational numbers}}Irrational numbers</span>start color maroonD, I, r, r, a, t, i, o, n, a, l, space, n, u, m, b, e, r, s, end color maroonD</span> are numbers that cannot be expressed as a fraction of two integers.Examples of irrational numbers:<span><span>-4\pi, \sqrt{3}<span>−4π,<span>√<span><span> 3</span> <span> </span></span></span></span></span>minus, 4, pi, comma, square root of, 3, end square root</span>How are the types of number related?The following diagram shows that all whole numbers are integers, and all integers are rational numbers. Numbers that are not rational are called irrational.
You can set up a system of equations for this problem. x= number of coach tickets and y = number of first class tickets.
$210x + $1200y = $10,230 (cost of coach ticket plus cost of first class tickets is total budget)
x + y = 11 (number of coach tickets plus number of first class tickets is total number of people)
Solve the second equation for y to get y = 11 - x, then plug that into the first equation and solve for x:
$210x + $1200(11 - x) = $10,230
$210x + $13,200 - $1200x = $10,230
-$990x + $13,200 = $10,230
-$990x = $2,970
x = 3
Sarah bought x = 3 coach tickets. Plug that into the second equation and solve for y:
3 + y = 11
y = 8
Sarah bought y = 8 first class tickets.
