Math Word Problem { SAT }

Question

Between 1497 and 1500, Amerigo Vespucci embarked on two voyages to the New World. According to Vespucci’s letters, the first voyage lasted 43 days longer than the second voyage, and the two voyages combined lasted a total of 1,003 days. How many days did the second voyage last? ( please make it simple and explain how you got the answer I’m lost )

Answer 1

We need to cut through all the info to find the actual math. The 2nd voyage lasted an unknown number of days, let's call it x. The first voyage lasts 43 more days, than the second, so it would take x+43 days. We know both voyages combined took 1003 days. So x + (x+43) = 1003. Simplify the left side, leaving us with 2x +43 = 1003. Then subtract 43 from both sides to isolate x, so 2x + 43 -43 = 1003-43. So 2x = 960 . Divide both sides by 2 to leave just x on the left, so 2x ÷2 ÷ 960 ÷2. So x= 480. The 2nd voyage took x or 480 days. The 1st voyage took x+43 or 481 +43= 523 days.

Check: 480+ 523= 1003.

Answer 2

Hi Sam,

This is a good problem on the SAT that translates between word problem and mathematical expression. Let's begin by choosing a variable to indicate the length of the second or first voyage. Let's call it v1 for voyage 1 and v2 for voyage 2.

Then let's write the system of equations, i.e. how are the two voyages related?

Well, voyage 1 is forty two days longer than voyage 2: v1=v2+42.

The second equation gives you the total length of both voyages: v2+v1=1003

This then becomes a substitution problem. Substitute for v1 in the second equation: v2+(v2+42)=1003

And solve the equation for the unknowns. You should be able to obtain your answer.

Best of luck studying,

Tytochrone Tim