What are a and b if their product is 240 and b is 4 less than twice a.

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

We need to find a and b.

Their product is 240

=> a*b = 240

bis 4 less than twice the value of a

=> b = 2a - 4

substitute in a*b = 240

=> a(2a - 4) = 240

=> 2a^2 - 4a - 240 = 0

=> a^2 - 2a - 120 = 0

=> a^2 - 12a + 10a - 120 = 0

=> a(a - 12) + 10(a - 12) = 0

=> (a + 10)(a -12) = 0

=> a = -10 and a = 12

b = -24 and b = 20

a and b can have the values (-10 , -24) and (12 , 20)

hala718's profile pic

hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted on

Given that the product of a and b is 240

Then we will rewrite:

a * b = 240 .............(1)

Now we know that b is 4 less than twice a.

Then we rewrite:

b= 2a - 4..............(2)

Now we will solve the system by substituting (2) into (1).

==> a* (2a-4) = 240

==> 2a^2 - 4a = 240

==> 2a^2 - 4a - 240 = 0

Now we will divide by 2.

==> a^2 - 2a - 120 = 0

==> Now we will factor:

==> (a-12)(a+10) = 0

==> a1 = 12 ==> b1 = 20

==> a2= -10 ==> b2= -24

Then we have two solutions:

The solution are : ( 12, 20) and (-10, -24)

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