Antonio travels 100 km at an average speed of x km/h.
He then travels a further 150 km at an average speed of (x+10) km / h.
The time taken for the whole journey is 4 hours 20 minutes.
Show that 13x2−620x−3000=0.
x100+x+10150=431 oe or 150=(313−x100)(x+10)x(x+10)100(x+10)+150x or better
300x+3000+450x=13x2+130x oe or better
Allow correct multiples of 13x2−620x−3000=0
Solve 13x2−620x−3000=0 to find the speed Antonio travels for the first 100 km of the journey.
You must show all your working and give your answer correct to 1 decimal place.
2(13)620±(−620)2−4(13)(−3000)
or equivalent quadratic formula
M1 for (−620)2−4×13×(−3000) oe
x=52.1 to 52.2 final answer
Reject negative speed
In a shop the cost of a fiction book is $ x and the cost of a reference book is $(x+2). The cost of 11 fiction books is the same as the cost of 10 reference books.
Find the value of x.
x=
20
M1 for 11x=10(x+2) oe
In another shop, the cost of a fiction book is $ y and the cost of a reference book is $(y+2). Maria spends $ 95 on fiction books and $ 147 on reference books.
She buys a total of 12 books.
Show that 6 y^2-109 y-95=0.
y95+y+2147=12
M2
M1 for y95 or y+214795(y+2)+147y=12y(y+2) oe
M1 for clearing their equation with algebraic fractions in y and y+2
leading to 6y2−109y−95=0
A1 with all brackets shown expanded and no errors or omissions
Find the value of y.
y=
19
Correct or FT their positive answer from factors dep on B1 earned
18 Solve.
2y−13y=43y=
−21 oe
B2 for 12y=6y-3 or better.
M1 for 4×3y=3(2y−1).