Systems of Equations by Substitution On the windowsill is a plant that is 3 inches tall. It is growing 3 inches per week. A second plant, which is 8 inches tall, is on a coffee table. It is growing 2 inches per week. Eventually, the two plants will be the same height. How tall will the plants be when they are the same height?

Second Part

On the windowsill is a plant that is 3 inches tall. It is growing 3 inches per week. A second plant, which is 8 inches tall, is on a coffee table. It is growing 2 inches per week. Eventually, the two plants will be the same height. How many weeks will it take them to be the same height?

Show steps please and thank you

70

step-by-step explanation:

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4

step-by-step explanation:

step 1: solve one of the equations for one of the variables. let's solve the first equation for y:

step 2: substitute that equation into the other equation, and solve for x.

step 3: substitute x = 4 x = 4 x=4 into one of the original equations, and solve for y.

answer: 8 years

step-by-step explanation:

the explanation is that in 8 years the child will be 20 and in 8 years the father will be 40 and 20 is half of 40.