# Simultaneous Linear Equations help

#### Mrs G30

##### New member
Hi,

I'm currently doing a level 3 BTEC mainly from home so I'm struggling with a few of my maths questions as i cant get in to see the tutor as much. i have figured most out but these 3 I have just totally stumped on, if anyone could offer me any help where to start or guide me to the right your tube video to learn i would really appreciate it so much! I think its because they have put it in a scenario format that twisted my brain.

Question is as follows;

Solve a pair of simultaneous linear equations in two unknows

(a) For a turned component it was found that if it was produced on a capstan lath the total cost was £40 for tooling plus 25P per component. On a CNC lathe the total cost was £150 for tooling plus 15P per component. Determine how many components need to be made to make the CNC machine a viable costed option.

(b) A manufacturer supplied oil for use in hydraulic systems. The oil is dispatched in drums or crates containing 12 cans. For an order of 5 drums and 12 crates, the transit cost amounts to £33.70. For 3 drums and 30 crates, the cost for transit £35.50. Find the transit cost for dispatching 1 drum and also 1 crate of cans.

(c) A flywheel is used to provide movement on a machine. At a time (t) seconds after the break is applied to the flywheel, the speed of the rotation (n) revolutions per minute is given as n=at +b, where a and b are constants. If n = 440 when t = 40 and n = 360 when t = 60, find the constants a and b. Also find out how long the break must be applied for before the flywheel comes to a stop.

#### Mrs G30

##### New member
I've got (c) set up as;

440 = (a x 40) + b

360 = (a x 60) + b

but i'm not sure where to go from here?

#### Subhotosh Khan

##### Super Moderator
Staff member
Hi,

I'm currently doing a level 3 BTEC mainly from home so I'm struggling with a few of my maths questions as i cant get in to see the tutor as much. i have figured most out but these 3 I have just totally stumped on, if anyone could offer me any help where to start or guide me to the right your tube video to learn i would really appreciate it so much! I think its because they have put it in a scenario format that twisted my brain.

Question is as follows;

Solve a pair of simultaneous linear equations in two unknows

(a) For a turned component it was found that if it was produced on a capstan lath the total cost was £40 for tooling plus 25P per component. On a CNC lathe the total cost was £150 for tooling plus 15P per component. Determine how many components need to be made to make the CNC machine a viable costed option.

(b) A manufacturer supplied oil for use in hydraulic systems. The oil is dispatched in drums or crates containing 12 cans. For an order of 5 drums and 12 crates, the transit cost amounts to £33.70. For 3 drums and 30 crates, the cost for transit £35.50. Find the transit cost for dispatching 1 drum and also 1 crate of cans.

(c) A flywheel is used to provide movement on a machine. At a time (t) seconds after the break is applied to the flywheel, the speed of the rotation (n) revolutions per minute is given as n=at +b, where a and b are constants. If n = 440 when t = 40 and n = 360 when t = 60, find the constants a and b. Also find out how long the break must be applied for before the flywheel comes to a stop.

#### lookagain

##### Elite Member
I've got (c) set up as;

440 = (a x 40) + b

360 = (a x 60) + b

but i'm not sure where to go from here?
For help for the first part of (c), write them as

440 = 40a + b
360 = 60a + b

Subtract the second equation from the first equation on your way
toward solving for a. Then substitute that back into one of the
original equations to work out b.

Staff member