Mrs. Johnson, wholoves to give parties, invited all her neighbors to a barbecue

Question

Mrs. Johnson, wholoves to give parties, invited all her neighbors to a barbecue lastnight.   The highlight of Mrs. Johnson’s parties isalways the delicious fruit punch. At her party last week, shemade a punch with 7-ounce cans of lemonade and 6-ounce cansof grape juice, using 10 cans in all. Last night Mrs.Johnson, using 3 more cans of grape juice than last week and8-ounce cans of orange juice instead of lemonade, made an ounceless punch than last week. She used whole number of cans oforange juice. How many? I need to know how many cans ofOrange juice used. Thanks for helping Mrs. Johnson, wholoves to give parties, invited all her neighbors to a barbecue lastnight.   The highlight of Mrs. Johnson’s parties isalways the delicious fruit punch. At her party last week, shemade a punch with 7-ounce cans of lemonade and 6-ounce cansof grape juice, using 10 cans in all. Last night Mrs.Johnson, using 3 more cans of grape juice than last week and8-ounce cans of orange juice instead of lemonade, made an ounceless punch than last week. She used whole number of cans oforange juice. How many? I need to know how many cans ofOrange juice used. Thanks for helping

Explanation / Answer

L=# lemonade cans G=#grape juice cans O=#Orange juice cans P1=amount of punch last week set up equations 7L+6G=P1 L+G=10---->7L+7G=70 subtract -G=P1-70---->P1=70-G 6(G+3)+8O=P1-1 --->6G+8O=P1-19--->P1=6G+8O+19 set P1s equal 70-G=6G+8O+19 --->51=7G+8O now just guess and check with integers what values of G and Osatisfy this equation. if O=1, 7G=43 which is not a multiple of 7.if O=2, 7G=35 which IS a multiple of 7, so O=2 and G=5. you canplug these back in to check

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