Each week Dan drives two routes, route X and route Y. One week he drives route X three times and route Y twice. He drives a total of 134 miles that week. Another week he drives route X twice and route Y five times. He drives a total of 203 miles that week. (a) Find the length of each route. route X = ..................... miles route Y = ..................... miles (b) State an assumption that has been made in answering part (a).

GCSE OCR Maths 3D trigonometry: Each week Dan drives two routes,

Each week Dan drives two routes, route X and route Y - OCR - GCSE Maths - Question 23 - 2017 - Paper 1

Question 23

Each week Dan drives two routes, route X and route Y. One week he drives route X three times and route Y twice. He drives a total of 134 miles that week. Another w... show full transcript

Worked Solution & Example Answer:Each week Dan drives two routes, route X and route Y - OCR - GCSE Maths - Question 23 - 2017 - Paper 1

Step 1

(a) Find the length of each route.

96%

114 rated

Answer

Let the length of route X be represented by $x$ miles and the length of route Y be represented by $y$ miles.

From the first week, we have:

Driving route X three times and route Y twice: $3x + 2y = 134 ag{1}$

From the second week, we have:

Driving route X twice and route Y five times: $2x + 5y = 203 ag{2}$

Now, we will solve these two equations to find the values of $x$ and $y$ .

Solve the equations:

Multiply equation (1) by 2: $6x + 4y = 268 ag{3}$
Multiply equation (2) by 3: $6x + 15y = 609 ag{4}$
Now, subtract equation (3) from equation (4): $(6x + 15y) - (6x + 4y) = 609 - 268$ $11y = 341$ $y = rac{341}{11} = 31 ext{ miles}$
Substitute $y = 31$ back into equation (1): $3x + 2(31) = 134$ $3x + 62 = 134$ $3x = 72$ $x = 24 ext{ miles}$

So, the lengths are:

route X = 24 miles
route Y = 31 miles

Step 2

(b) State an assumption that has been made in answering part (a).

99%

104 rated