Question 1110556
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(1) {{{B+N+P+W = 14}}}  the total number of days was 14 (two weeks)
(2) {{{120B+200N+80P+100W = 2020}}}  the total cost for lodging was $2020
(3) {{{N = B+W}}}  the number of days spent in NYC was the same as the sum of the days spent in Boston and DC
(4) {{{N = 3P}}}  they spent three times as many days in NYC as they did in Philly<br>
Four equations, four unknowns.<br>
With 4 equations in 4 variables, there are always many different ways to find the answer.  Here is what I did....<br>
{{{120B+200N+80P+100W = 2020}}}
{{{(100B+100W)+(200N)+80P+20B = 2020}}}  I separated the 120B into 100B+20B so I could use equation (3)
{{{100N+200N+80P+20B = 2020}}}
{{{300N+80P+20B = 2020}}}
{{{900P+80P+20B = 2020}}}
(5) {{{980P+20B = 2020}}}<br>
With this equation (5), knowing that B, N, P, and W are whole numbers less than 14, there is only one possible value for P: P=2.  Then it follows immediately that B=3.  Equation (4) then gives N=6; and equation (1) then gives W=3.<br>
Answer: Philly 2, Boston 3, New York 6, Washington DC 3.