We can use elimination for these set of systems. First, we need to set up our variables. Belts=b Hats=h Now, the situation is 6 belts and 8 hats for $140. The situation after is 9 belts and 6 hats for $132. Let’s set up our system of equations. 6b+8h=140 9b+6h=132 We need to eliminate a variable. Since b has coefficients of 6 and 9, we can easily eliminate b by multiplying the top equation by 3 and the bottom by -2. 18b+24h=420 -18b-12h=-264 Now let’s add. 12h=156 Let’s divide to get h by itself. 156/12=13=h So a hat costs $13. We need to put in 13 for one of the equations so we can find the cost of a belt. 9b+6(13)=132 9b+78=132 We need b by itself. 9b=54 54/9=6 Belts are $6 We can also use the first equation to check our answers. 6(6)+8(13) 36+104 140. So, the price of a belt is $6 while the price of a hat is $13.
The tree grows 6cm per year and we need to find out how long it will take to grow 1 meter. We know that 1 meter is equal to 100 centimeters. So: 6x = 100 x = 16.67 It will take 16.67 years (or one and two-thirds of a year) for the tree to reach 1 meter.
