The manager of a garden store ordered two different types of marigold seeds for her display. The first type cost her $1 per packet and the second kinds cost $1.26 per packet. How many packets of the first type did she purchase if she bought 50 more of the $1.26 packets than the $1 packets and spent a total of $402?
Let x = the amount of marigolds at $1 per packet. Let y = the amount of marigolds at $1.26 per packet. Because there are 50 more packets of the $1.26 seeds than the $1 seeds, y = x + 50. Use the equation 1x + 1.26y = 420 to ?nd out the total number of packets of each. Through substituting into the second equation, you get 1x + 1.26(x + 50) = 402. Multiply on the left side using the distributive property: 1x + 1.26x + 63 = 402. Combine like terms on the left side: 2.26x + 63 = 402. Subtract 63 from both sides: 2.26x + 63 - 63 = 402 - 63. Simplify: 2.26x =339. Divide both sides by 2.26: 2.26x/2.26 = 339/2.26; so, x = 150 packets, that is the number of packets that costs $1 each.