(05.06) a bicycle manufacturing company makes a particular type of bike. each child bike requires 4 hours to build and 4 hours to test. each adult bike requires 6 hours to build and 4 hours to test. with the number of workers, the company is able to have up to 120 hours of building time and 100 hours of testing time for a week. if c represents child bikes and a represents adult bikes, determine which system of inequality best explains whether the company can build 10 child bikes and 12 adult bikes in the week. no, because the bike order does not meet the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100

The company can build 10 child bikes and 12 adult bikes in the week .

Step-by-step explanation:

Let 'c' be the number of child bike and 'a' be the number of adult bike.

According to the problem

The restriction of building time for a week is 4c+6a≤120 hours(1)

and the restriction of testing time for a week is 4c+4a≤100 hours(2)

Lets check whether company can build c=10 and a=12 bikes in a week by putting this value in (1) and (2)

(1)4(10)+6(12)=40+72=112≤120 ⇒Restriction of building time is satisfied.

(2)4(10)+4(12)=40+48=88≤100⇒Restriction of testing time is satisfied.

Hence,  the company can build 10 child bikes and 12 adult bikes in the week,as order is meeting with the restrictions.

he used the algebra tiles correctly.

step-by-step explanation:

given : 3x(2x-1)

solution :

since he used algebra tiles .

armando's solution is the same in the solution shown in figure

as he distributed 2x into x and x and wrote them vertically

and also write   -1 vertically

and 3x into x and x and x and wrote it horizontally

performing the multiplication in the algebra tiles we get

and solving the given expression :

3x(2x-1)

since solving the expression using tiles   and solving the expression algebraically we get the same answer

thus   we can choose the first statement as the answer to this problem which is "he used the algebra tiles correctly".